bl 



VARIATION IN ACHIEVEMENT 

AND ABILITY WITHIN 

THE GRADES 



BY 

S. C. GARRISON, PH.D. 



GEORGE PEABODY COLLEGE FOR TEACHERS 

CONTRIBUTION TO EDUCATION 

NUMBER EIGHT 




PUBLISHED UNDER THE DIRECTION OF 

GEORGE PEABODY COLLEGE FOR TEACHERS 

NASHVILLE, TENN. 
1922 



t^0t50«!rftP^ ^ 



'^^^^, 

"? ^■i:'^^ 



VARIATION IN ACHIEVEMENT 

AND ABILITY WITHIN 

THE GRADES 






/ 



BY 



SI C. GAKRISOIS, PH.D. 



GEORGE PEABODY COLLEGE FOR TEACHERS 

CONTRIBUTION TO EDUCATION 

NUMBER EIGHT 




PUBLISHED UNDER THE DIRECTION OF 

GEORGE PEABODY COLLEGE FOR TEACHERS 

NASHV ILLE, TENN. 
1922 



CONTENTS 
PART I 

PAGE 

1. Introduction 5 

2. The Problem 6 

3. The Subjects 7 

4. The Field 8 

5. The Tests 9 

6. Procedure in Giving the Tests 11 

7. Scoring the Results 12 

8. Scholastic Records 12 

9. Method of Studying the Data 12 

PART II 

1. The Data 15 

2. Final Scores 16 

PART III 

1. Central Tendency and Variabilty for Each Grade and Group. _ 20 

2. Relation Between Teachers' Judgment and Test Results 22 

3. Relation Between Accomplishment and Accuracy 24 

4. Relation Between Accomplishment and School Standing 25 

5. Relation Between Teachers' Judgment and Accomplishment 26 

PART IV 

1. Comparison of Results with Those Obtained with Others 36 

Binet, Carmen, Smedley, Gesell, Bolton, Freeman, Bon- 
ser, Lapie, Keys, Winch, Kelley, Wallin, Mead, Pintner. 

PART V 

Summary and Conclusions 44 

A. As to Procedure 44 

B. As to Results 44 

References 46 

Bibliography of Tests 47 



PART I 

1. Introduction* 

During the past few years much psychological investiga- 
tion has been made into the nature and amount of individual 
differences: Before the publication in 1883 of Galton's 
"Inquiries into the Human Faculties and Its Development," 
the work done had been only of a general nature. Up to 
that time psychological conceptions had been based largely 
upon data secured from investigations made upon the men- 
tal processes by which we know and recognize the physical 
world. 

Since that time much has been done in the standardiza- 
tion of tests for the measurement of mental and physical 
abilities. Also a large number of scales have been devel- 
oped by means of which the problems arising in education 
are studied. Methods of applying these standardized tests 
and of handling the results secured in a scientific way have 
been developed. This whole field of endeavor is but a part 
of a much larger one which has during the last century been 
extending and applying science to all phases of life. 

Ever since Galton announced the results of his investiga- 
tions, this field has been a fruitful source of experimenta- 
tion. A number of investigations have been made simply 
for their scientific interests. Others have been made with 
a view of discovering the causes for certain social and moral 
conditions. And yet others have been undertaken in which 
the work was confined principally to school children, with 
the hope that the results might aid in solving some of the 
pressing educational problems. These studies have been 
confined for the most part to children in the upper grades, 
or to college students, and a major portion of the work 
devoted to younger children has dealt with physical rather 
than mental abilities. Probably the most fruitful work in 
the field of individual difference for the educator interested 
in children in the lower grades has come as a by-product 
of investigations aimed primarily along other lines. Just 
now much work is being done with educational tests. Vari- 
ations in the achievement of pupils, and even classes and 
schools, are being measured. 

The studies on the question of mental ability and its rela- 
tion to school work have been very fragmentary. The 
bright school child has been neglected by most investiga- 
tors. Perhaps one reason for this lies in the fact that many 



*This study was made during the school year of 1917-1918. Its completion was 
delayed by the World War. 



6 Variation Within the Grades 

studies have been made by those not directly interested in 
school work. A very large number of investigations have 
been made with reference to the relations existing between 
low mentality and the social vices. This question has been 
a very pressing one, and it is but natural that new methods 
of investigation should first be applied where apparently 
the need is greatest. 

It is important that the school know the individual dif- 
ferences and possibilities of the children it is trying to 
educate; it should know what abilities exist and how they 
are distributed ; it should know how many dull, normal, and 
bright children there are, how they are distributed, and 
where each child ranks on a definite scale of values. It 
is extremely important that no social or educational hin- 
drances be permitted to handicap the development of chil- 
dren of unusual ability. 

Perhaps the most frequent criticism of the ordinary 
grammar school is that it subjects all pupils to the same 
conditions. Only in a few schools is provision made for 
superior ability. Pupils of different abilities are subjected 
to the same conditions. They take the same course of 
study for the same period of time and are promoted to- 
gether. Even the time of promotion is fixed beforehand 
without any regard to the differences in ability represented 
in the grade. 

2. The Problem 

This investigation has been undertaken with a view to 
obtaining facts on educational questions which arise be- 
cause of individual differences in the ability of grammar- 
school children. It is an attempt to help solve some of the 
everyday educational problems which arise because of indi- 
vidual differences in pupils. We wish to study the differ- 
ence in the various abilities of children, some of whom stand 
at the top of the class and others at the bottom. Are the 
children at the head of the class stronger in some special 
ability than those at the bottom ? In what abilities are the 
children at the bottom of the class weakest? Where is 
there greater variability with reference to mental ability — 
at the top or the bottom of the class? What relation is 
there between mental ability and standing in the grades? 
These are some of the questions we wish to hold in mind 
throughout the study. It is hoped that the study will con- 
tribute something to method, in that we will be better able 
to judge the abilities of the various groups within the 
grades. It is hoped also that the study will contribute 
something to school organization, inasmuch as we will no- 
tice the overlapping of mental ability. 



Variation Within the Grades 7 

3. The Subjects 

The subjects used in this investigation were the children 
of the fourth, fifth, sixth, and seventh grades of the Pea- 
body Demonstration School. Only those children who had 
been in the school for a year or more and who had been 
fairly regular in attendance were used. No attempt was 
made to select the children because of class standing. The 
only factors used in the selection, as stated above, were reg- 
ularity of attendance and enrollment in the school for at 
least a year before the study was made. As a matter of 
fact, most of the children taking the tests had been attend- 
ing the school three years. In all, 108 children — 43 boys 
and 65 girls — were used. These were divided between the 
four grades, as follows : fourth, 24 ; fifth, 24 ; sixth, 30 ; and 
seventh, 30. They were divided according to sex as fol- 
lows: fourth, 10 boys and 14 girls; fifth, 8 boys and 16 
girls; sixth, 14 boys and 16 girls; and seventh, 11 boys and 
19 girls. Tables la to Ic show the distribution of the chil- 
dren used in the study according to age, sex, group (each 
group contains approximately one-fourth of the grade) , and 
grade. Age has been considered here as meaning the age 
of the child at his last birthday. 

TABLE la 
Distribution of Children by Grades, Ages, and Sexes 

Boys Girls 

Age Gr. IV V VI VII T. IV V VI VII T. G. T. 

9 to 10 32005 9100 10 15 

10 to 11 60208 36009 17 

11 to 12 13318 2741 14 22 

12 to 13 3 8 3 14 1 12 5 18 32 

13 to 14 00145 0109 10 15 

14 to 15 3 3 4 4 7 

Grand total 10 8 14 11 43 14 16 16 19 65 108 

TABLE lb 
Distribution of Children by Grades, Groups, and Sexes 

Boys Girls 

Grade G. 1 G. 2 G. 3 G. k T. G. 1 G. 2 G. 3 G. i, T. G. T. 

IV 3 2 2 3 10 3 4 4 3 14 24 

V 22228 4444 16 24 

VI 3 4 4 3 14 4 4 4 4 16 30 

VII 1 4 2 4 11 6 4 6 3 19 30 

Grand total 9 12 10 12 43 17 16 18 14 65 108 

TABLE Ic 

Average Age and Variability of Each Grade 

Boys 
Av. A. D. 
Grade Yrs. Mos. Mos. 

IV 10 4 7 

V 11 2 11 

VI 12 0.6 8 

VII 13 3 8.7 



Girls 


Whole G. 


Av. A. D. 


Av. A. D. 


Yrs. Mos. Mos. 


Yrs. Mos. Mos. 


9 11 5.6 


10 1 6.0 


11 1 9 


11 1.3 9.7 


12 3 4.8 


12 1.8 6.3 


13 2 7.5 


13 2.6 8 



8 Variation Within the Grades 













TABLE Id 






T 








Average 


Age of Each 


Group 






Grade 

IV 

V 

VI 

VII 


Yrs. 

10 

11 

12 

13 


G. 


1 

Mos. 

n 

i 

5 


4. 


G. 2 
Yrs. Mos. 
10 
10 7 

12 2 

13 2 

The Field 


G. 

Yrs. 

9 

11 

12 

13 


3 
Mos. 

9 

8 

3 

8 


G. 4 

Yrs. Mos. 

9 9 

11 6 

11 8 

13 



The field chosen for this study was the Peabody Demon- 
stration School. This school is run in connection with 
George Peabody College for Teachers, and was under the 
direct supervision of Dr. Thomas Alexander, Professor of 
Elementary Education. The course of study covers the 
usual course found in the South. It, however, includes 
much more than is usually found in a twelve-grade course 
of study. Only the fourth, fifth, sixth, and seventh grades 
were used in this study. 

The school draws its pupils from the best homes in the 
city. Its population is largely American. The homes from 
which the children come would compare favorably in wealth, 
social status, and intelligence with those of any city. The 
positions held by the fathers of the children are of a very 
varied nature. The following professions are the most fre- 
quent ones: banker, broker, city and state official, lawyer, 
manufacturer, and minister. 

The fact that the school is dependent upon the tuition re- 
ceived from the pupils guarantees the hearty cooperation 
of its patrons. This fact will also attest to the character of 
the work of the school. Parents do not withdraw their 
children from public schools where tuition is free and where 
a good social atmosphere is prevalent to place them in a 
private school where there is a tuition fee, unless they feel 
that there is a distinct advantage in doing so. Further- 
more, the school always has a very large waiting list. Par- 
ents make application for the enrollment of their children 
months ahead. Owing to limited facilities, only about 350 
children can be provided for. 

In a sense, the school receives only pupils from a select 
group. However, a close examination will reveal the fact 
that this selection is not from one class of pupils, but from 
all the classes usually found in a large number of children. 
First, there are those parents who feel that their children 
are able to do exceptional work, and want to give them the 
very best advantages possible. Second, there are those who 
know that their children are not progressing in the public 
schools as they should and who desire to place them where 
they will be given special attention by well-trained teachers. 



Variation Within the Grades 9 

Then there is a third group who send their children to a 
private school simply because they are able to do so. 

At no time are the grades in the school overcrowded. 
There are simply as many pupils as there are sittings in 
each room ; and there is one teacher for every grade, except 
in the upper grades, where the work is on the departmental 
plan. Specialists teach swimming, sewing, music, and man- 
ual training. All recesses are taken on the playground 
every day in the year, except in rain or snow. The chil- 
dren have access to the college campus and gymnasium. 
There is nothing fixed or formal about promotions, except 
that the pupil must prove his ability to go ahead. A spirit 
of cooperation between parent and teacher such as is sel- 
dom seen is prevalent in the school work. 

5. The Tests 

A. Educational. — The first group of tests consisted of a 
number of educational tests. These tests were used in a 
survey of the Peabody Demonstration School during the 
spring of 1917. A part of the data secured in that survey 
has been used in this study. The children were promoted 
at the end of the session, and the grade to which they were 
promoted has been used throughout this study as their 
school grade. The tests employed in that survey, the data 
of which have been included here, consisted of two arith- 
metic tests, two reading tests, one writing test, and one 
spelling test. Two of the tests — one of arithmetic and one 
of reading — were given again in the spring of 1918. It 
was originally intended that all the tests should be given 
again in the spring of 1918, and the study based upon a com- 
parison of the two sets of data. Owing to the fact that the 
writer entered the United States Army, this was not found 
possible. No detailed description of the tests has been 
given here. This may be found in the case of any of the 
tests by referring to the bibliography. 

One of the arithmetic tests used was that devised by 
Woody ('16). This arithmetic scale consists of two series, 
A and B, each four in number — one each for addition, sub- 
traction, multiplication, and division. The A series was 
used in this investigation. These scales were devised to 
measure achievement in the fundamentals of arithmetic, 
either of an individual, of a class, or of a whole school sys- 
tem. The Courtis ('14) arithmetic tests consist of a num- 
ber of series subdivided into several forms. Form 2, Series 
B, was used in this study. This group of tests was devised 
by Courtis to provide a general measure of the four funda- 
mental abilities in arithmetic. 



10 Variation Within the Grades 

The spelling scale used was the one devised by Ayers 
('15) for measuring spelling ability throughout the grades. 
This consists of a series of lists of words, the words in any 
list being approximately equal in difficulty. Three lists 
were used with each grade. Lists L, 0, and I were used 
with the fourth grade ; L, 0, and Q, with the fifth ; 0, S, and 
Q, with the sixth ; and Q, S, and U, with the seventh. Thus 
there are always two lists by means of which any grade 
may be compared with another grade immediately above or 
below it. 

For the reading tests the Thorndike ('14) and the Kan- 
sas Silent Reading Tests were used. The Thorndike Read- 
ing Test used was one of four which Thorndike proposed to 
work out for testing reading. ability. It is really a test of 
the pupil's knowledge of words. The Kansas Silent Read- 
ing Test was devised by Kelly ('15) to measure both speed 
and accuracy in reading. His purpose in devising the test 
was to secure one which would measure the ability to read 
and follow directions. 

The handwriting scale used was the one devised by Thorn- 
dike ('10) for measuring legibility and speed in handwrit- 
ing. 

B. Mental. — The mental tests used are not described in 
detail, because they can readily be found by turning to the 
proper reference. Practically all the tests have been used 
in other investigations. The series consisted of tests of 
memory, perception, association, and invention tests of a 
linguistic nature. The memory tests were divided into six 
groups — three of logical memory, two of rote memory for 
concrete words, two of rote memory for abstract words, 
four of rote memory for related words, four of rote memory 
for unrelated words, and two of rote memory for digits. 
The logical memory tests used were: (1) The Marble 
Statue, as in Whipple ('15) ; (2) The Man and His Wagon, 
as devised by Miss Margaret Hart and used by Strong 
('16) ; and (3) The Boy and a Piece of Cake, as devised and 
used by Strong ('16). 

Pyle's ('13) lists of concrete and abstract words were 
used. The following lists of words were selected for the 
memory for related word tests : 



table 


holly 


winter 


school 


chair 


bells 


ice 


teacher 


rug 


gifts . 


river 


book 


picture 


toys 


cold 


desk 


bed 


candy 


sled 


pen 


dresser 


tree 


skate 


read 


trunk 


chimney 


water 


write 


clock 


sled 


melt 


spell 


brush 


merry 


brook 


ink 


light 


deer 


flow 


word 



Variation Within the Grades 



11 



The following four lists of unrelated words were also 
used: 



music 


ship 


tree 


sick 


water 


cap 


bed 


long 


shoe 


mouse 


never 


white 


paper 


ring 


green 


run 


goat 


button 


die 


cloth 


noise 


chalk 


turkey- 


arm 


house 


turkey- 


break 


match 


cloud 


street 


dog 


stamp 


knife 


hand 


moon 


inch 


flag 


snail 


watch 


city 



The memory-for-digits test consisted simply of groups 
of digits, Whipple's ('15) procedure being followed. 

The perception tests were divided into two groups — (1) 
the A test and (2) the digit test — as devised by Wood worth 
and Wells ('11). Two tests were given in marking letters 
and four in marking digits. Trabue's ('16) completion 
test (numbers B, C, D, and E) was used as a part of the 
test for inventiveness. The word-building test as proposed 
by Whipple ('15) was used as the other. Pyle's ('13) four 
lists of words for the opposites test were used for that test. 

6. Procedure in Giving the Tests 

The educational tests were each given on a different day, 
and all the grades took the test on the same day. No set 
time was used. The experimenter simply made arrange- 
ment with the principal and went from grade to grade giv- 
ing the tests. Wherever it was possible for one grade to 
disclose useful information concerning the test to another 
grade, the test was so given that only grades having taken 
the test or not having taken it were together at recess. 
There were apparently no cases of cheating. The tests 
were not given to grades below the fourth. Pupils who 
were absent did not receive an opportunity to take the edu- 
cational tests at a later time. 

As a rule, the procedure used in giving the mental tests 
was the same as that used in giving the educational tests. 
The only objects sought in giving instructions were to keep 
conditions uniform and to have the children thoroughly un- 
derstand what was expected of them. It was desired to 
keep the conditions under which the children took the tests 
as near like actual schoolroom conditions as possible. For 
that reason all the tests were given to the pupils at their 
desks. All the pupils in each grade were given the tests, 
because it was feared that idle pupils might disturb those 
working at the tests. However, only the papers of those 
having taken the educational tests were scored. 



12 Variation Within the Grades 

In a few cases where a pupil was absent when a test was 
given, the test was taken later. So far as the examiner 
could discern, the tests were taken in a spirit of eagerness 
and fairness. 

7. Scoring the Results 

The method adopted in scoring the results of the educa- 
tional tests was in each case that set forth by those who 
had standardized the test. This rule was adhered to 
throughout. In scoring the results of a mental test, meth- 
ods already in use, which seemed to be reliable, were used. 
In case of a mental test where no method had been gener- 
ally adopted, the one used was that which seemed the fairest 
and which seemed to vary as little as possible from results 
secured by other methods of scoring. 

8. Scholastic Records 

In order to compare the results secured from the tests 
with class standing in each school subject, all the grades in 
each subject for the school year 1916-17 were compiled. 
From these a ranking was made. In grading the pupils, 
the following letters were used by the teachers : E, G, F, U, 
and VP. E is given to pupils doing the best work, while 
VP denotes work which is unsatisfactory. Theoretically 
and in actual practice most of the pupils receive the marks 
G, F, and U. The pupils are so ranked and graded that 
over a long period of time the grades will fall in a normal 
surface of distribution. Since the letters have no definite 
values, the ordinary values attached to such school grades 
were substituted. Wherever a minus or plus sign was 
attached to a letter, this was taken into account. A rank- 
ing was made for each month's work, and from these rank- 
ings a combined ranking was made for the year. While the 
method of changing group grades to rankings for any one 
month would be very gross, it was thought that a fairly 
accurate ranking could be secured when a number of rank- 
ings based on a year's work were used. 

9. Method of Studying the Data 

A. Ranking the Pupils.— The name of each pupil used in 
each grade was written on a slip of paper and several teach- 
ers asked to rank the child according to ability. The teach- 
ers were asked to rate them not alone on school work, but 
as they saw them in the home and on the playground as 
well. For the fourth and fifth grades, only two rankings 
were available; for the sixth and seventh grades, three 
rankings were used. In no case did any teacher know 



Variation Within the Grades 13 

where any child had been placed by another teacher until 
all the rankings were made. Every teacher who ranked 
the children had taught or was then teaching the grade. 
From these several rankings of each grade a combined 
ranking was made. In making the combined ranking, all 
the positions given each child were added and a new rank- 
ing made from these totals, the child with the least total 
being placed first and the one with the greatest last. 

B. The Groups. — In making the study it was desired 
first of all to keep the conditions as they are actually found 
in school work. For that reason, instead of selecting three 
groups (one making most progress, one making average 
progress, and one making least progress) from the four 
grades combined, it was thought best to study the four 
grades themselves, making four groups within each grade. 
The children in each grade have been grouped according to 
the teachers' rankings. These groups have been designated 
as G. 1, G. 2, G. 3, and G. 4. G. 1 is the best 25% in each 
grade and G. 4 the poorest, according to the teachers' judg- 
ment. In studying these various groups, IV G. 1 has been 
used to designate the best group in the fourth grade. Sim- 
ilarly for the other groups. In case the number of children 
in any grade was not divisible by four, the extra children 
were placed in the G. 2 and G. 3 groups. This was the 
case in the sixth and seventh grades. 

C. The Measures Employed. — It was the aim of the in- 
vestigation to study the individual rather than the group 
wherever possible. For that reason, as many facts con- 
cerning each individual as space would permit have been 
included in the tables. Any child's score, or his standing, 
in any or all of the tests may readily be found. However, 
from the standpoint of time and space, it would be physically 
impossible to study each child thoroughly. It was, there- 
fore, necessary to compare groups rather than individuals. 
In making these comparisons, several measures were em- 
ployed. The average (Av.) was used as a measure of cen- 
tral tendency. The Pearson Coefficient of Variability 

[A^ was used as a measure of variability. For deter- 

, Av. J 

mining the relationships of abilities, the coefficient of cor- 
relation derived from the method of differences in relative 

r , 6 s um D'^ 1 , , 
position or ranks \r=l— ^^(n^—i)} '^^^ "^^^ ^^^^• 

The percentage of one group reaching or surpassing a 
given point in another group, or a given point in a total 
array of the scores for the four grades, has been used for 



14 Variation Within the Grades 

showing the differences between groups in the same test. 
This gives a value easily found, and its meaning is clear. 
Thus the percentage of pupils in one group who equal or 
surpass the highest 25% of another group, or of all the 
groups combined, is frequently used. 

As a measure of position or rank attained by a pupil, the 
percentile or quartile has been used. Thus the best 25% 
of the pupils in a grade is designated as the first quartile 
(G. 1) or as those above the 75 percentile. G. 1, G. 2, G. 3, 
and G. 4 each contain one-fourth of the children in a grade, 
ranked from best to poorest. In this study wherever the 
term '"quartile" is used, it is meant to designate a certain 
group of children or scores made by that group. The term 
'"percentile" is used to designate a point in a total array of 
scores. The 75 percentile is that point above which the 
best one-fourth of the class falls. 



PART II 
1. The Data 

The final scores in each of the tests are arranged in Ta- 
bles II to V, inclusive. The original material is of such 
amount that it was deemed best not to try to reproduce it 
all here. This is on file in the Jessup Psychological Labo- 
ratory. The scores have been distributed in the tables by 
grades and groups. As the tables are presented, each 
grade is divided into four groups. Each of the groups com- 
prises approximately one-fourth of the grade. The num- 
ber given any pupil in the tables designates his position in 
the grade according to the judgment of the teachers rating 
him. Thus, pupil number one in the fourth grade was 
rated by the teachers of that grade as the best pupil in 
that grade. By this method of distribution we are able to 
determine as far as our data permit the attainment for the 
best fourth (G. 1) of each grade, the next best fourth 
(G. 2) , and so on. The sex of any pupil may be determined 
by reference to the tables. The age of each pupil is given 
with the final scores. 

The data are presented in tables, then, so as to show: 
(1) the complete results of each test; (2) the final score 
given any child in any test; and (3) the rating, from best 
to poorest, given the pupils by the teachers. 



16 



Variation Within the Grades 



2. Final Scores 

TABLE II 
Fourth Grade (IV) 





Educational Tests 


Mental Tests 




A .r. 














Memory 


Tests 














Ages 
























bfi 






ft 






m 

5 


CO 

C 


<u 

'•B 
a 

u 

o 


u 


'3) 


s 




0) 

u 


% 
u 
■*-> 
CO 


to 




'3 

u 
o 


o 
'-5 
S 
"a 
S 


CO 


Oh 

o 


CO 

u 


-5 

c 
o 


Si 

1 

ft 




cS 


o 


cS 


ji 


>. 


o 


ii 


C 


o 


•a 




cd 


? 





ft 


6 




O 


W 


H 


< 


h3 


« 


? 


o 


< 


5 


O 


o 


o 


1 


10 


8 


17 


18.4 


8.8 


51 


101 


20 


16 


74 


62 


7 


86 


37 


52 


29 


2 


9 


11 


19 


18.4 


9.4 


58 


92 


25 


14 


87 


70 


7 


80 


44 


51 


25 


3 


11 


4 


25 


13.9 


7.0 


59 


73 


27 


22 


77 


71 


7 


100 


43 


46 


20 


4 


11 


4 


11 


15.4 


8.6 


49 


102 


22 


17 


76 


66 


6 


111 


37 


52 


32 


5 


10 


10 


17 


18.5 


8.2 


53 


82 


25 


21 


80 


65 


7 


127 


44 


56 


33 


6 


9 


2 


19 


20.2 


8.8 


54 


90 


22 


12 


86 


64 


6 


118 


27 


58 


37 


7 


9 


11 


25 


16.1 


8.8 


55 


97 


30 


23 


82 


67 


6 


130 


33 


51 


25 


8 


10 





15 


8.6 


7.6 


55 


86 


24 


20 


82 


72 


7 


85 


43 


54 


43 


9 


9 


8 


20 


18.5 


6.6 


58 


78 


15 


14 


62 


53 


7 


83 


21 


50 


15 


10 


9 


6 


16 


18.4 


6.6 


53 


68 


28 


17 


82 


72 


6 


153 


38 


43 


29 


11 


10 


6 


11 


13.2 


6.6 


53 


85 


21 


16 


75 


64 


6 


115 


28 


51 


28 


12 


10 


4 


13 


10.2 


6.4 


51 


104 


19 


13 


73 


57 


6 


98 


28 


55 


27 


13 


10 





11 


6. 


7.0 


43 


64 


20 


14 


64 


50 


6 


72 


29 


49 


25 


14 


9 


7 


11 


19.5 


5.8 


43 


85 


18 


15 


70 


61 


6 


72 


23 


47 


26 


15 


9 


2 


5 


5.3 


6.4 


51 


68 


21 


15 


62 


52 


5 


100 


27 


41 


22 


16 


9 





3 


11.5 


6.8 


34 


66 


18 


19 


65 


47 


6 


80 


32 


45 


23 


17 


10 


6 


2 


10.4 


5.2 


45 


63 


18 


14 


71 


56 


5 


68 


25 


35 


23 


18 


11 





11 


7.6 


6.6 


54 


53 


17 


11 


61 


48 


6 


102 


32 


44 


19 


19 


9 





10 


12.8 


5.8 


40 


68 


16 


15 


55 


50 


7 


72 


31 


39 


25 


20 


10 





22 


9.7 


6.4 


34 


60 


21 


16 


49 


39 


5 


59 


30 


40 


31 


21 


9 


8 


9 


8.8 


6.8 


32 


60 


16 


15 


36 


32 


6 


101 


27 


39 


18 


22 


9 


2 


10 


9.1 


5.9 


38 


42 


18 


13 


56 


30 


6 


80 


21 


48 


25 


23 


9 


8 


10 


11.9 


6.0 


52 


52 


19 


10 


59 


47 


5 


70 


25 


44 


22 


24 


9 


9 


9 


6.5 


4.8 


36 


41 


21 


12 


50 


42 


6 


52 


14 


44 


21 



^This score was secured by adding the scores made in each of the four fundamental 
operations. 

-This score is the total of the individual scores. 



Variation Within the Grades 



17 



TABLE III 
Fifth Grade (V) 



Educational Tests 








Mental 


Tests 




























Memory 


Tests 














Ag 


es 




























M 






















'a 

3 
Ph 

o 

d 






< 

u 
3 
o 
O 


< 

O 
O 


P3 

ci 

C 
i4 


■3 

c 

u 
o 


■XI 

41 
U 

<; 


•3 

c 

u 
o 

JS 

El 


"i 


'3 
Pi 


+-> 

S 
% 

u 

c 

t3 


u 

V 

o 
O 


u 

03 

< 


5 


c 
y 


C 

"3 


c 

"ft 

B 





•JO 


09 
U 


c 
o 


0) 

•1 

ft 



1 


10 


11 


35 


439 


20.3 


9.4 


58 


10 


127 


32 


27 


98 


86 


7 


166 


58 


61 


35 


2 


11 


11 


27 


450 


19.9 


10.2 


54 


11 


109 


33 


26 


85 


81 


7 


139 


53 


66 


43 


3 


11 


1 


36 


460 


16.7 


10.2 


57 


11 


97 


30 


23 


88 


71 


8 


189 


57 


56 


36 


4 


9 


7 


20 


386 


12.8 


8 


53 


10 


119 


20 


20 


84 


75 


7 


112 


45 


57 


49 


5 


10 


6 


23 


329 


21.7 


10.1 


56 


11 


126 


28 


15 


108 


74 


8 


164 


47 


58 


50 


6 


11 





24 


371 


18.4 


10.2 


60 


9 


95 


23 


20 


80 


76 


8 


119 


55 


54 


35 


7 


11 





24 


310 


16.7 


8.6 


59 


10 


106 


24 


15 


86 


66 


7 


139 


62 


57 


37 


8 


11 


6 


15 


335 


18.4 


10.1 


57 


9 


104 


23 


16 


79 


74 


6 


153 


55 


56 


37 


9 


11 


6 


15 


305 


14.4 


8.6 


50 


8 


69 


20 


22 


68 


80 


7 


183 


24 


57 


43 


10 


10 





22 


278 


6.2 


7.6 


51 


9 


96 


23 


18 


69 


67 


7 


124 


43 


53 


38 


11 


9 


6 


20 


322 


14.8 


9.4 


59 


10 


101 


31 


17 


86 


93 


6 


186 


37 


53 


39 


12 


10 





18 


302 


14.8 


8.6 


43 


9 


83 


28 


19 


78 


67 


7 


107 


29 


45 


31 


13 


9 


7 


9 


268 


19.7 


9.4 


54 


9 


74 


19 


12 


62 


61 


6 


96 


24 


48 


36 


14 


12 


.4 


12 


317 


15 


9 


54 


12 


98 


23 


16 


69 


69 


7 


149 


21 


54 


26 


15 


12 


3 


9 


282 


10.4 


10 


54 


9 


104 


27 


22 


67 


66 


6 


113 


34 


54 


32 


16 


12 


5 


14 


340 


9.0 


8.4 


55 


14 


80 


19 


19 


80 


48 


7 


110 


17 


44 


29 


17 


12 


5 


14 


320 


11.3 


10 


50 


14 


64 


17 


14 


74 


79 


7 


121 


31 


52 


29 


18 


11 


1 


12 


298 


6.2 


7.2 


50 


12 


66 


18 


18 


76 


60 


6 


92 


28 


53 


31 


19 


10 


2 


12 


187 


13.4 


5.6 


39 


12 


70 


18 


19 


69 


53 


7 


80 


32 


55 


23 


20 


12 


1 


11 


268 


15.5 


6 


39 


11 


66 


22 


11 


59 


60 


7 


77 


26 


49 


27 


21 


11 


7 


11 


239 


13.1 


9 


52 


11 


93 


27 


20 


77 


63 


7 


99 


28 


44 


34 


22 


10 


3 


8 


251 


12.5 


7.6 


48 


8 


79 


18 


10 


66 


57 


6 


98 


19 


41 


34 


23 


11 


8 


2 


250 


3.9 


6.8 


53 


2 


74 


19 


12 


70 


56 


6 


74 


8 


45 


25 


24 


13 


2 


5 


221 


12.5 


8 


45 


5 


29 


17 


6 


73 


63 


6 


72 


29 


38 


29 



^This score is the sum of the scores made in each of the four fundamental operations. 



18 



Vai^iation Within the Grades 



TABLE IV 

Sixth Grade (VI) 



Educational Tests 



Mental Tests 





! 


















Memory 


Tests 














Ages 




























n 






















o. 






< 

3 


< 

O 

o 




OJ 

c 
o 




(V 

c 

u 
O 


Is 




-a 
u 


u 


o 

u 

CO 




c 
'+3 


'3 


o 
S 




3 


i 

00 

u 
03 


T. 

Si 
-(J 

c 


o 


d 


01 


o 


O 


^ 


<s 


A 


>> 


Ji 


o 


"o! 


c 


Q 


.a 




C8 


* 


o 


o. 


'A 


>^ 


s 


O 


\< 


H 


< 


H 


a 


« 


p 


o 


<! 


5 


O 


^ 


O 


O 


1 


12 


10 


33 


503 


25.4 


9.6 


58 


11 


119 


30 


21 


109 


96 


8 


137 


55 


61 


40 


2 


12 


6 


36 


611 


18.4 


10.7 


58 


12 


117 


26 


21 


84 


79 


7 


165 


54 


61 


32 


3 


12 


4 


32 


567 


18.4 


9.4 


54 


11 


114 


28 


27 


83 


83 


7 


148 


41 


57 


33 


4 


12 


3 


32 


576 


25.4 


9.4 


60 


11 


99 


30 


23 


87 


72 


7 


205 


51 


58 


37 


5 


12 


3 


30 


517 


12.9 


9.4 


43 


10 


94 


27 


21 


83 


64 


6 


160 


56 


48 


30 


6 


12 


. 7 


28 


544 


17.3 


10.1 


60 


12 


119 


30 


22 


79 


72 


6 


159 


44 


57 


37 


7 


12 


1 


25 


563 


12.6 


9.4 


49 


12 


107 


26 


19 


78 


65 


7 


172 


50 


60 


37 


8 


12 


1 


9 


490 


12.4 


9.8 


53 


9 


87 


25 


19 


82 


77 


5 


118 


53 


57 


28 


9 


10 


7 


18 


501 


25.4 


8.0 


55 


11 


94 


24 


18 


96 


93 


7 


151 


44 


56 


29 


10 


12 


10 


25 


550 


10.6 


10.4 


44 


10 


118 


28 


23 


92 


68 


8 


134 


46 


52 


27 


11 


11 


5 


5 


367 


18.3 


8.2 


53 


10 


121 


25 


17 


82 


85 


7 


147 


35 


60 


41 


12 


12 


5 


13 


476 


15.8 


9.4 


53 


9 


94 


22 


23 


75 


77 


7 


122 


55 


58 


26 


13 


11 


10 


19 


480 


25.4 


8.8 


43 


10 


94 


26 


17 


91 


75 


7 


211 


48 


54 


27 


14 


13 


5 


20 


490 


6.3 


8.8 


58 


10 


93 


24 


16 


81 


71 


6 


123 


40 


56 


29 


15 


12 


11 


17 


480 


19.7 


9.6 


52 


9 


77 


22 


12 


72 


52 


7 


101 


40 


48 


33 


16 


11 


9 


13 


485 


17.1 


8.6 


44 


10 


90 


23 


16 


81 


49 


6 


107 


33 


50 


40 


17 


12 





26 


366 


16.1 


10.1 


57 


8 


88 


28 


20 


93 


80 


7 


126 


45 


52 


33 


18 


11 


10 


15 


416 


8.9 


9.4 


56 


10 


62 


26 


24 


88 


60 


7 


131 


15 


56 


30 


19 


12 


9 


22 


505 


10.6 


8.6 


46 


12 


117 


25 


19 


88 


62 


6 


142 


46 


55 


30 


20 


12 


9 


5 


452 


15.4 


10 


43 


10 


90 


27 


21 


95 


56 


6 


102 


45 


49 


30 


21 


12 


10 


11 


353 


13.4 


8.8 


56 


9 


88 


26 


18 


80 


71 


7 


97 


38 


53 


30 


22 


12 


11 


17 


478 


10.6 


8.0 


56 


11 


77 


21 


15 


82 


84 


5 


138 


17 


51 


31 


23 


11 


10 


16 


487 


13.4 


6.6 


46 


9 


91 


20 


15 


75 


66 


5 


142 


32 


48 


29 


24 


12 


5 


18 


390 


17.3 


9.6 


39 


9 


97 


28 


19 


89 


65 


5 


116 


46 


53 


33 


25 


10 


5 


16 


497 


16.1 


7.6 


36 


7 


51 


21 


9 


75 


50 


5 


71 


44 


47 


36 


26 


11 


2 


18 


480 


12.2 


10.1 


53 


13 


88 


24 


20 


64 


74 


6 


128 


36 


57 


33 


27 


12 


5 


10 


460 


8.5 


5.0 


35 


9 


92 


24 


21 


88 


45 


6 


108 


43 


52 


18 


28 


12 


3 


8 


451 


21.4 


10 


47 


9 


91 


24 


20 


81 


72 


7 


101 


31 


55 


40 


29 


12 





21 


553 


16.1 


7.2 


44 


9 


76 


21 


16 


87 


65 


6 


106 


36 


48 


33 


30 


11 





8 


408 


6.3 


8.6 


48 


8 


63 


17 


2 


63 


42 


6 


85 


39 


47 


16 



Vai'iation Within the Grades 



19 



TABLE V 

Seventh Grade (VII) 











Educational Tests 










Mental 


Tests 




























Memory 


Tests 














Ages 


































'ft 






< 


< 




P2 




a; 




^ 


T3 
01 




^ 
-<-> 




c 


c 

is 

'3 


c 


3i 


CM 

o 
d 

iz; 






OJ 


r/3 


-4-> 

c 
o 


y. 

u 

o 
O 


o 

o 


03 
09 

C 


'5 
c 

o 


m 
u 
>> 
< 


c 

u 
o 

X 


13 

u 
O 


73 

"a! 


c 


u 

C 
o 
O 


a 

u 

< 


OB 

'So 

Q 


C 
cS 


'C 
u 

o 


"a 

S 

o 

O 


'a 

O 

a 
O 


1 


14 





46 


680 


34.6 


11 


55 


11 


113 


31 


22 


92 


82 


9 


153 


59 


70 


42 


2 


12 


4 


36 


632 


16.1 


11 


59 


11 


112 


26 


23 


95 


79 


8 


184 


33 


66 


51 


3 


12 


5 


25 


641 


12.8 


10 


47 


10 


107 


28 


24 


101 


84 


7 


127 


38 


65 


27 


4 


13 


3 


62 


643 


22.5 


n 


55 


11 


121 


31 


21 


95 


82 


7 


191 


45 


60 


57 


5 


12 


7 


33 


598 


23.4 


9 


49 


9 


121 


28 


25 


91 


85 


7 


193 


32 


56 


41 


6 


13 


7 


28 


539 


32.3 


10 


49 


10 


129 


26 


26 


99 


97 


7 


183 


57 


66 


46 


7 


12 


9 


35 


600 


22.3 


10 


46 


10 


117 


26 


16 


86 


62 


7 


173 


54 


64 


48 


8 


13 


4 


42 


590 


14.8 


9 


44 


9 


80 


26 


27 


96 


70 


8 


158 


42 


53 


44 


9 


14 


7 


28 


500 


8.5 


9 


34 


9 


91 


28 


20 


101 


78 


7 


218 


35 


53 


49 


10 


13 


11 


25 


444 


17.5 


6 


41 


6 


106 


21 


17 


82 


62 


8 


138 


41 


59 


26 


11 


14 


2 


25 


492 


18.4 


8 


43 


8 


99 


27 


21 


86 


63 


7 


149 


26 


57 


38 


12 


11 


10 


40 


580 


26.3 


10 


49 


10 


117 


24 


20 


85 


89 


8 


167 


43 


58 


47 


13 


11 


4 


22 


513 


10.9 


8 


29 


8 


107 


24 


21 


80 


57 


7 


118 


33 


53 


36 


14 


12 


1 


30 


593 


14.8 


10 


51 


10 


104 


27 


21 


85 


62 


8 


178 


42 


58 


39 


15 


14 


4 


18 


498 


11.1 


9 


49 


9 


71 


21 


17 


78 


59 


7 


120 


39 


53 


24 


16 


13 


1 


31 


578 


18.1 


9 


43 


9 


87 


22 


9 


76 


55 


7 


218 


31 


50 


43 


17 


14 


4 


1 


264 


14.4 


12 


43 


12 


89 


22 


15 


75 


60 


7 


113 


28 


51 


42 


18 


13 


7 


19 


443 


21.0 


8 


37 


8 


94 


24 


19 


86 


71 


7 


115 


13 


49 


40 


19 


13 


6 


20 


573 


8.4 


8 


38 


8 


101 


22 


21 


77 


60 


7 


155 


26 


52 


26 


20 


13 


10 


17 


362 


8.1 


11 


24 


11 


67 


19 


15 


74 


65 


5 


101 


25 


47 


18 


21 


14 


2 


18 


369 


13.4 


10 


44 


10 


105 


23 


18 


69 


56 


7 


208 


32 


52 


33 


22 


13 


7 


22 


519 


13.5 


10 


54 


10 


95 


21 


14 


81 


71 


7 


141 


42 


56 


29 


23 


13 


2 


18 


490 


13.4 


10 


46 


10 


70 


25 


15 


84 


85 


7 


177 


45 


44 


30 


24 


13 





15 


497 


19.1 


10 


57 


10 


100 


24 


16 


88 


75 


7 


172 


35 


53 


42 


25 


13 


5 


29 


506 


14.3 


11 


58 


11 


99 


23 


15 


61 


60 


6 


173 


25. 


46 


33 


26 


12 


10 


32 


514 


9.1 


9 


26 


9 


96 


21 


13 


76 


55 


6 


113 


25 


34 


21 


27 


12 


4 


9 


338 


10.7 


10 


52 


10 


98 


21 


14 


75 


55 


6 


112 


41 


54 


43 


28 


14 





26 


465 


26.1 


8 


21 


8 


93 


19 


17 


73 


62 


7 


164 


21 


51 


29 


29 


13 





21 


369 


13.8 


9 


42 


9 


91 


19 


19 


63 


57 


7 


135 


22 


46 


30 


30 


12 


5 


11 


469 


14.4 


9 


30 


9 


69 


15 


9 


74 


55 


6 


125 


28 


42 


27 



PART III ^ 

Interpretation of Results 

1. Central Tendency and Variability for Each Grade and 
Group. — The central tendency and variability for each 
grade and group are given in Tables VIA to VIM for each 
test. From an examination of the tables it is seen that 
G. 1 in each grade surpasses the whole grade and the other 
groups of that grade in each test except the Thorndike 
handwriting test. In 39 cases out of 49, G. 2 surpasses 
G. 3 and G. 4 of the same grade. In 40 cases out of 49, 
G. 4 makes a poorer average score than either of the other 
groups of the grade. The most striking thing in these re- 
sults is that in a majority of cases the best group in a grade 
surpasses the second best group in the grade immediately 
above. For example, G. 1 of the sixth grade surpasses 
G. 2 of the seventh grade in 10 cases out of 13. In 7 cases 
out of 13 the tables show less absolute difference between 
G. 1 of the seventh grade and G. 1 of the fourth grade than 
between G. 1 and G. 4 of the seventh grade. 



TABLE VI 

Central Tendency and Variability by Grades and Groups for 

Each Test 









A. Courtis 


Arithmetic 


Tests 












Whole G. 


G. 1 


G. 2 




G. 


3 


G 


. 4 






A.D. 


A.D. 


A.D. 






A.D. 




A.D. 


Grade 


Av. 


Av. 


Av. Av. 


Av. Av. 




Av. 


Av. 


Av. 


Av 


VII 


29.8 


.36 


42.0 .3 


34.2 .1 




22.2 


.37 


21.5 


.4 


VI 


24.4 


.3 


36.0 .2 


22.0 .2 




20.9 


.2 


18.3 


.17 


v 


21.8 


.44 


38.0 .2 


23.7 .18 




13.1 


.3 


11.7 


.2 


IV 


13.4 


.39 


18.0 .13 
B. Woody 


16.7 .24 
Arithmetic 


Tests 


7.2 


.54 


11.7 


.3 




Whole G. 


G. 1 


G. 2 




G. 


3 


G 


. 4 






A.D. 


A.D. 


A.D. 






A.D. 




A.D. 


Grade 


Av. 


Av. 


Av. Av 


Av. Av. 




Av. 


Av. 


Av. 


Av. 


VII 


508 


.13 


619 .05 


526 .08 




442 


.21 


451 


.12 


VI 


483 


.1 


555 .05 


479 .06 




443 


.18 


462 


.08 


V 


314 


.16 


406 .1 


309 .03 




304 


.06 


263 


.09 








C. Thorndike Reading 


Tests 












Whole G. 


G. 1 


G. 2 




G. 


3 


G. 


. 4 






A.D. 


A.D. 


A.D. 






A.D. 




A.D. 


Grade 


Av. 


Av. 


Av. Av. 


Av. Av. 




Av- 


Av. 


Av. 


Av. 


VII 


8.4 


.1 


9.7 .03 


8.7 .06 




7.8 


.14 


1.1 


.07 


VI 


9. 


.1 


9.7 .05 


9.1 .07 




8.8 


.07 


8.3 


.18 


V 


8.6 


.14 


9.7 .06 


8.8 .07 




8.8 


.13 


7.2 


.12 


IV 


7.0 


.14 


8.5 .07 


7.1 .09 




6.3 


.08 


5.9 


.08 








D. Kansas Silent Reading Tests 










Whole G. 


G. 1 


G. 2 




G. 


3 


G. 


4 






A.D. 


A.D. 


A.D. 






A.D. 




A.D. 


Grade 


Av. 


Av. 


Av. Av. 


Av. Av. 




Av. 


Av. 


Av. 


Av 


VII 


21.2 


.27 


28.3 .24 


23.9 .14 




15.7 


.36 


17.2 


.29 


VI , 


18.7 


.18 


21.7 .09 


19.2 .13 




18. 


.27 


15.9 


.19 


V 


18.5 


.34 


23.3 .17 


19. .4 




19. 


.34 


12.8 


.19 


IV 


12.9 


.31 


17.5 .1 


14.1 .24 




10.1 


.36 


9.8 


.19 



Variation Within the Grades 



21 



Whole G. 
A. D. 



Grade 


Av. Av. 


VII 


42.8 .17 


VI 


49.2 .15 


V 


52.5 .1 


IV 


48. .18 




Whole G. 




A.D. 


Grade 


Av. Av. 


VII 


9.5 .11 


VI . 


10.0 .11 


V 


9.8 .03 




Whole G. 




A.D. 



Grade Av. Av. 

VII 86.3 .12 

VI 59.8 .13 

V 55.8 .16 



E. Ayres Spelling Tests 

G. 1 G. 2 

A. D. A. D. 



G. 3 
A. 



D. 



Av. 

51.4 

52. 

56.3 

54. 



Av. 

.08 
.1 
.04 
.06 



Av. 

42.5 

50.5 

53. 

54. 



Av. 

.14 

.11 

.1 

.06 



Av. 
41. 
50.6 
53. 
45. 



Av. 
.15 
.11 
.05 
.13 



F. Thorndike Handwriting Test- 



G. 1 
A.D. 



G. 2 
A.D. 



Av. Av. 

10.3 .06 

11.3 .05 

10.3 .07 



Av. Av. 

8.6 .01 

9.7 .06 
9.1 .05 



-Legibility 

G. 3 
A.D. 

Av. Av. 

9.7 .12 

9.8 .1 
9.1 .05 



G. Thorndike Handwriting Test — Speed 



G. 1 

A. 



D. 



Av. 
83.4 
70 
55.2 



Av. 
.11 
.11 
.16 



G. 2 
A.D. 



Av. 
88.6 
56.2 
53.7 



Av. 
.16 
.1 
.11 



Av. 
85.1 
56.3 
63.3 



3 
A.D. 

Av. 
.15 
.16 
.15 



Av. 
36.6 
43. 
46. 

42. 



G. 4 
A.D. 

Av. 
.32 
.13 
.11 

.12 



G. 4 
A.D. 



Av. 
9.4 
9.1 
9.0 



Av. 
.08 
.12 
.05 




H. Logical Memory Tests 



Whole G. 
A.D. 

Grade Av. Av. 

VII 97.0 .13 

VI 93.6 .14 

V 87.6 .2 

IV 68.5 .25 



G. 1 
A.D. 



Av. 
117 
109 
108 
87.1 



Av. 
.05 
.08 
.09 

.08 



G. 2 
A.D. 



Av. 
97 
97.2 
93.1 

81 



Av. 
.13 
.12 
.11 
.09 



Av. 



81 
60.1 



G. 3 

A. D. 

Av. 
.12 
.11 
.16 
.12 



G. 4 
A.D. 



Av. 
88.5 
79.7 
68.5 
45.7 



Av. 
.14 
.18 
.2 
.21 



Whole G. 
A. D. 



Grade 


Av. 


Av. 


VII 


192.3 


.12 


VI 


196.7 


.08 


V 


185.2 


.11 


IV 


164 


.14 




Whole G. 






A.D. 


Grade 


Av. 


Av. 


VII 


35.3 


.24 


VI 


41.9 


.18 


V 


35 


.34 


IV 


30.8 


.2 




Whole G. 






A.D. 


Grade 


Av. 


Av. 


VII 


53.9 


.11 


VI 


53.8 


.07 


V 


52.1 


.1 


IV 


47.2 


.11 




Whole G. 






A.D. 



Grade Av. 
VII 155 

VI 133 
V 123 

IV 91 



Av. 
.18 
.11 
.11 
.23 



I. Rote Memory for Words Tests 

G. 2 G. 3 



G. 1 
A.D. 



Av. 
221 
212 
215 
185 



Av. 
45.4 
50.1 
47.5 
38.7 



Av. 
64 
57.4 
58.5 
52.2 



Av. 
172 
164 
148 
104 



Av. 
.06 
.07 
.07 
.06 



Av. 

199.4 

202 

191.5 

196.5 



2 
A.D. 

Av. 
.08 
.06 
.03 
.1 



J. Word-Building Tests 



G. 1 
A.D. 



G. 2 
A.D. 



Av. 
.21 
.09 
.12 
.11 



Av. 
37.6 
45.1 
41.7 
32 



Av. 
.12 

.12 

.28 

9 



K. Completion Tests 



G. 1 
A.D. 



G. 2 
A.D. 



Av. 
.05 
.04 
.06 
.06 



Av. 

55.5 

55 

53.5 

50.6 



Av. 
.04 
.05 
.06 
.06 



L. Cancellation Tests 

G. 1 G. 2 

A. D. A. D. 



Av. 
.1 
.09 
.15 
.1 



Av. 
156 

138 
150 

108 



Av. 
.16 
.17 
.15 
.22 



Av. 

181.6 

194.5 

172 

149.5 



A.D. 

Av. 
.07 
.06 
.05 
.06 



G. 3 

A.D. 



Av. 
30.2 
34 
26 

28 



Av. 

50 

51.8 

50.8 

43.5 



Av. 
153 
123 
113 
83 



Av. 
.24 
.27 
.2 
.11 



G. 3 
A.D. 



Av. 
.05 
.05 
.06 
.09 



G. 3 
A.D. 



Av. 
.23 
.12 
.11 
.14 



G. 4 
A.D. 



Av. 
172 
178 
161 
124.5 .09 



Av. 
.07 
.09 
.06 



G. 4 
A.D. 



Av. 
26.7 
39.3 
23.7 
24.7 



Av. 
.3 
.11 
.3 
.19 



Av. 
46.4 
51.3 
45.3 
42.3 



G. 4 
A.D. 

Av. 
.11 
.07 
.09 

.07 



Av. 

142 

108 

84 

69 



G. 4 
A.D. 

Av. 
.16 
.11 
.12 
.22 



22 Variation Within the Grades 



M. Opposites Tests 

Whole G. G. 1 G. 2 G. 3 G. 4 

A. D. A. D. A. D. A. D. A. D. 



Grade Av. Av. Av. Ax\ Av. Av Av. Av. Av. Av. 

VII 36.7 .23 44.5 .15 38 .18 32.6 .22 32.1 .18 

VI 31.6 .11 35.1 .08 30 .12 31.6 .09 29.8 .2 

V 34.5 .12 41.1 .15 37.5 .07 30.5 .08 28 .12 

IV 26 .17 29.3 .16 28 .2 23 .07 23.6 .14 

2. Relation Between Position Held in the Grade, Accord- 
ing to Teachers' Judgment, and Position Held in the Four 
Grades Combined, According to the Results of the Tests. 

TABLE VII 

Per Cent of the Scores Made by Each Grade and Group Falling 

Between Certain Points in a Total Array of the 

Educational Test Scores Combined 







Above 75 


50 to 75 


25 to 50 


Below 25 


Grade and Group 


Percentile 


Percentile 


Percentile 


Percentile 


VII 


G. 1 


71.4 


28.6 






VII 


G. 2 


50.0 


37.5 


12.5 




VII 


G.3 


37.5 


12.5 


25.0 


25.0 


VII 


G.4 


28.6 


14.3 


28.6 


28.6 


VII 


W. G. 


46.7 


23.3 


16.7 


13.3 


VI 


G. 1 


57.1 


28.6 


14.3 




VI 


G.2 


25.0 


50.0 


25.0 




VI 


G.3 


12.5 


37.5 


25.0 


25.0 


VI 


G.4 


28.6 


14.3 


28.6 


28.6 


VI 


W. G. 


23.3 


43.3 


20.0 


13.3 


V 


G. 1 


50.0 


33.3 


16.7 




V 


G.2 


33.3 


16.7 




50.0 


V 


G.3 


33.3 


16.7 


16.7 


33.3 


V 


G.4 






83.3 


16.7 


V 


W. G. 


29.1 


16.7 


29.1 


25.0 


IV 


G. 1 




33.3 


66.7 




IV 


G.2 




16.7 


50.0 


33.3 


IV 


G.3 




16.7 




83.3 


IV 


G.4 






16.7 


83.3 


IV 


W. G. 




16.7 


33.3 


50.0 



Table VII shows the average position the members of 
each grade and group hold in a total array of all the edu- 
cational test scores for the four grades combined. For 
the seventh grade, 71.4 per cent of the members of G. 1 
fall in the best 25 per cent of the scores as compared to 
46.7 per cent for the whole grade. Similarly we have 57.1 
and 23.3 per cents for the sixth grade and 50 and 29.1 per 
cents for the fifth grade, while no pupil in the fourth grade 
attained a position in the best 25 per cent of all the scores. 
No pupil in the G. 1 groups made a score falling in the poor- 
est 25 per cent of all the scores, while for the whole grades 
we have the following per cents falling in that group: 
seventh, 13.3 ; sixth, 13.3 ; fifth, 25 ; and fourth, 50. 



Variation Within the Grades 23 

So far as these tests are a measure of ability in school 
subjects, the results show plainly the superiority of the G. 1 
groups over the others. If we should neglect the present 
grades and attempt to regroup the children into four 
groups based on ability shown in these tests, the results 
show that the following per cents would be taken from each 
grade for each of the four new groups (No. 1 being the best 
group) : 

Group Seventh Grade Sixth Grade Fifth Grade Fourth Grade 

1 46.7 23.3 29.1 

2 23.3 43.3 16.7 16.7 

3 16.7 20.0 29.1 33.3 

4 13.3 13.3 25.0 50.0 

TABLE VIII 

Per Cent of the Scores Made by Each Grade and Group Falling 

Between Certain Points in a Total Array of the 

Mental Test Scores Combined 







Above 75 


50 to 75 


25 to 50 


Below 25 


Trade and Group 


Percentile 


Percentile 


Percentile 


Percentile 


VII 


G. 1 


85.7 


14.3 






VII 


G.2 


50.0 


25.0 


25.0 




VII 


G.3 


25.0 


25.0 


37.5 


12.5 


VII 


G. 4 


14.3 


28.6 


28.6 


28.6 


VII 


W.G. 


43.3 


23.3 


23.3 


10.0 


VI 


G. 1 


57.1 


42.9 






VI 


G.2 


37.5 


25.0 


25.0 


12.5 


VI 


G.3 


12.5 


37.5 


37.5 


12.5 


VI 


G.4 


14.3 


28.6 


28.6 


28.6 


VI 


W.G. 


30.0 


33.3 


23.3 


13.3 


V 


G. 1 


50.0 


33.3 


16.7 




V 


G.2 


33.3 


33.3 


16.7 


16.7 


V 


G.3 




33.3 


33.3 


33.3 


V 


G.4 




16.7 


16.7 


66.7 


V 


W.G. 


20.0 


29.2 


20.9 


29.2 


IV 


G. 1 




33.3 


33.3 


33.3 


IV 


G.2 




16.7 


50.0 


33.3 


IV 


G.3 






33.3 


66.7 


IV 


G.4 






16.7 


83.3 


IV 


W.G. 




12.5 


33.3 


54.2 



The position the members of each grade and group hold 
in a total array of the combined mental tests scores is shown 
in Table VIII. An examination of the table shows a con- 
siderable overlapping both between the grades and between 
the groups. Taken by grades, the best 50 per cent of all the 
pupils is made up as follows: 66.7 per cent of the seventh 
grade, 63.3 per cent of the sixth grade, 50.1 per cent of the 
fifth grade, and 12.5 per cent of the fourth grade. As a 
rule, the members of G. 1 and G. 2 tend to fall above the 



24 Variation Within the Grades 

median, while the members of G. 3 and G. 4 tend to fall 
below it. The poorest 27 children of the 108 children come 
from the four grades in the following per cents: seventh, 
10 ; sixth, 13.3 ; fifth, 29.2 ; and fourth, 54.2. If we should 
attempt to regroup the children of the four grades into four 
new groups based on ability shown in the mental tests, each 
grade would contribute the per cents shown in the summary 
below to the new groups : 



Group 


Seventh Grade 


Sixth Grade 


Fifth Grade 


Fourth Grade 


1 


43.3 


30.0 


20.0 




2 


23.3 


33.3 


29.2 


12.5 


3 


23.3 


23.3 


20.9 


33.3 


4 


10.0 


13.3 


29.2 


54.2 



3. Relation Between Accomplishment and Accuracy. — 
For the purpose of studying the relation between accom- 
plishment and accuracy we have taken for accomplishment 
the combined score for each of the tests before allowance 
has been made for errors on the basis mentioned when the 
method of scoring the tests was given in detail. As a meas- 
ure of accuracy, we have taken the total number of errors 
made in each test. In some tests, as the opposites test, 
where the score is simply the number of opposites given, we 
have tabulated the number of wrong responses, and these 
have been included here. The pupil making fewest abso- 
lute errors in any test has been considered best in point 
of errors in that test. A positive correlation in this case 
indicates that there is a tendency for accomplishment to be 
accompanied by accuracy. It should be noticed that the 
coefficient of correlation has no significance in several 
cases. In the Ayres spelling test and the Thorndike read- 
ing test each pupil attempted all the words given. In these 
cases there should be a perfect correlation between the num- 
ber of errors made and score. A somewhat higher coeffi- 
cient would have been found in each case if we had used the 
relative number of errors instead of absolute errors. 

TABLE IX 
Correlation Between Accomplishment and Accuracy 

Test Coefficient 

Courtis Arithmetic 54 

Kansas Silent Reading 52 

Logical Memory 47 

Rote Memory for Words 34 

Cancellation 10 

Word Building 23 

Opposites 28 

It should be noticed that these coefficients are the average 
secured for the four grades. In the case of the cancella- 



Variation Within the Grades 25 

tion and word-building tests, several of the grades gave 
small negative coefficients. On the whole, there appears to 
be a positive relationship between accomplishment and ac- 
curacy. The difference in the relationship between accom- 
plishment and accuracy in the educational tests and the 
mental tests can partially be explained. In the educational 
tests, especially the arithmetic tests, the pupils have had 
much previous work where accuracy has been emphasized. 
In the rote memory for word tests there was no central 
controlling idea as in the logical memory tests ; consequently 
more irrelevant ideas came to hand. The fact that none 
of the pupils had done similar tasks to the rote memory 
for words tests, while they had done similar work to the log- 
ical memory tests, probably explains the difference in the 
relation between accomplishment and accuracy in the two 
tests. In the cancellation tests there had been no previous 
practice; consequently there was no adjustment between 
speed and accuracy. Previous work in school doubtless 
aided in the word-building and opposites tests. 

TABLE X 

Average Rank in Accuracy Held in the Grade by the Members of 

Each Group 

Grade G. 1 G. 2 G. 3 G, U 

VII 4.3 13.6 17.7 24 

VI 5.6 14.3 16.6 25.6 

V 5.2 10.2 15.2 19.3 

IV 4.2 9.2 17 19.7 

In Table X is shown the average position each group 
holds in the grade in accuracy. The results were secured 
by making a combined ranking of all the absolute errors 
of the nine series of tests. This was done for each grade 
by first making a ranking for each test. These rankings 
were then combined by adding the numbers representing 
the ranks each pupil held in all the tests. The sums thus 
obtained were rearranged, and the pupil holding the small- 
est total was given first place. The errors from the Ayres 
spelling test and the Thorndike reading test were included 
in the totals from which the final ranking was secured. 
These tend to make a somewhat higher correlation than 
would otherwise be expected. It is seen from the table 
that the best groups in each grade surpass in accuracy the 
other groups of the grade. Likewise G. 4 is surpassed by 
all the other groups of the grade. 

4. Relation Betiveen Accomplishment and School Stand- 
ing. — For the purpose of studying the relation between ac- 
complishment in the tests and class standing we have com- 
bined the scores for each of the tests after allowance has 



26 Variation Within the Grades 

been made for errors as described in Part I. The class 
standing of each pupil is determined by the grades he re- 
ceived in each subject during the school year. The method 
by which each pupil's relative standing in the grade was 
secured is given in Part I. 

TABLE XI 

Correlation Between Accomplishment in the Educational 
Tests and School Standing 

Grade IV V VI VII 

No. of Cases 2i. 2i 30 30 Av. 

Courtis A. and Arithmetic 42 78 73 51 61 

Woody A. and Arithmetic 59 62 60 60 

Thorndike Handwriting and Penmanship 74 62 51 62 

Kansas S. R. and Reading 68 67 52 22 52 

Thorndike Reading and Reading 57 50 28 47 45 

Ayres Spelling and Spelling 31 77 50 69 57 

An exarnination of Table XI shows the relation between 
the educational tests and class standing in the correspond- 
ing school study. The coefficients are fairly high in each 
case. 

A combined ranking has been made from the separate 
rankings in the different school subjects. Likewise a com- 
bined ranking has been made for the mental tests. These 
have been correlated and the following coefficients of corre- 
lation found for the grades : 

Fourth Grade 73 

Fifth Grade 71 

Sixth Grade 67 

Seventh Grade 61 

Average 68 

A similar combination of the rankings of the educational 
tests gives the following coefficients of correlation when 
correlated with school standing: 

Fourth Grade 75 

Fifth Grade 83 

Sixth Grade 58 

Seventh Grade 71 

Average 72 

5. Relation Between Teachers' Judgment and Accom- 
plishment. — The pupils in each of the four grades used in 
the study were rated from best to poorest by the several 
teachers who had taught or were teaching the grades. 
These rankings were then combined, and the new ranking 
has been used throughout the study, the rank each pupil 
held having been given him as his number in the grade. 
For purposes of comparison, the rank of the pupils in each 
test has been given. 



Variation Within the Grades 27 

TABLE XII 

Correlation Between Teachers' Judgment and Accomplishment 

IN THE Educational Tests 

Fourth Grade 79 

Fifth Grade 81 

Sixth Grade 75 

Seventh Grade 70 

Average 74 

It should be noticed that in securing these coefficients a 
great number of tests have been used. For the fourth 
grade nine individual tests were used. Fourteen individual 
tests contributed to the figures from which the coefficients 
were derived for each of the fifth, sixth, and seventh grades. 

Table XIII gives the coefficients secured when accom- 
plishment in the mental tests is correlated with teachers' 
judgment. Thirty-four individual measurements contrib- 
uted to the figures representing accomplishment. Each co- 
efficient is, therefore, partially determined by each of a large 
number of measurements. 

TABLE XIII 

Correlation Between Teachers' Judgment and Accomplishment 

IN THE Mental Tests 

Fourth Grade 83 

Fifth Grade 79 

Sixth Grade 80 

Seventh Grade 74 

Average 79 

It is significant that there is higher correlation between 
attainment in the mental tests and teachers' judgment than 
between attainment in the educational tests and teachers' 
judgment. This probably can be explained by the fact that 
a much greater number of mental tests were used, thereby 
tending to more nearly equalize errors. Again, the teach- 
ers were requested to rate the pupils according to ability, 
regardless of classroom results. 

Terman ('16) found a coefficient of 48 between teachers' 
judgment and IQ's. He asked the teachers to rate the pu- 
pils on a scale of five, and this ranking was correlated with 
the result secured when the children were tested with the 
Stanford Revision of the Binet-Simon Scale. Terman and 
Binet ('11) are inclined to beheve that teachers are unable 
to rate children with any degree of accuracy. This is prob- 
ably true when children are rated in the abstract on a five- 
point scale (as Terman instructed his teachers) as (1) very 
bright, (2) bright, (3) average, (4) dull, and (5) very dull. 
Our results show that teachers are able to rate children by 



28 Variation Within the Grades 

comparison with other children with a surprising degree of 
accuracy. 

TABLE XIV 

Average Rank Attained in the Grade by the Members of Each 
Group in the Educational Tests 



Grade 


G. 1 


G.2 


G. 3 


G.U 


VII 


4.6 


15.3 


20.1 


21.1 


VI 


4.2 


15.4 


18 


23.1 


V 


4.5 


11.3 


13 


21.1 


IV 


5 


9.1 


18.1 


17.5 



It is seen from Table XIV that G. 1 in every grade has a 
higher relative position than either of the other groups of 
the grade. Similarly, G. 4 for each grade except the fourth 
has a lower relative position than the other groups of the 
grade. There is very little difference in the relative posi- 
tions held by G. 2 and G. 3 of the fifth grade. 

Table XV shows the average position the members of 
each group hold in their grades in the mental tests. Here, 
as stated before, 34 measurements determine the figures 
upon which the rankings are based. G. 1 in each grade 
holds a higher average position than the other groups of 
the grade. G. 4 holds a position inferior to the other 
groups. 

TABLE XV 

Average Rank Attained in the Grade by the Members of Each 
Group in the Mental Tests 



Grade 


G.l 


G.2 


G. 3 


G.A 


VII 


4.7 


12.6 


20.6 


23.6 


VI 


5.3 


13.1 


20 


22.8 


V 


4 


9.7 


15.8 


20.7 


IV 


5.5 


7.5 


16.8 


20.1 



Variation Within the Grades 29 

TABLE XVIa 
Fourth Grade (IV) 

Rank of Pupils in the Different Tests 



c. 


u 


3 


< 


Ph 


aj 


o 


■ij 














^ 


y 



S o sc c 



^ 5 



5 2 5 -^ 



SCto Sooj'-aaa — 

£o^ MsccsSac 



1 


7.5 


6 


3 


13 


3 


9 


2.5 


12 


6.5 


5.5 


6.5 


5 


2 


5.5 


6 


1 


2.5 


5 


4.5 


5 


17 


1.5 


8 


13 


3 


3 


1.5 


10 


8.5 


1 


12 


3 


2.5 


9.5 


3.5 


14 


21 


7 


4 


14 


9 


5 


14 


2 


7 


10 


6 


6.5 


5.5 


4 


6 


5 


7.5 


3.5 


6 


9 


10 


6 


1 


3 


1.5 


2 


3 


1 


6 


5.5 


1 


3 


6.5 


6 


10 


18 


4 


17 


1 


2 


4 


7 


1.5 


8 


3 


4.5 


4 


1 


10 


2 


8 


8 


13 


2 


8 


10 


20 


7 


4.5 


7 


4.5 


6.5 


13 


3.5 


4 


1 


8 


9 


4 


3.5 


13.5 


2.5 


11 


16 


4 


15 


22.5 


10 


14 


11 


10 


9 


6 


13.5 


9 


14 


2 


10 


1 


5 


19 


6.5 


9 


11 


14 


11 


13.J) 


9 


8.5 


8 


9.5 


5 


14.5 


8 


8 


10 


12 


11 


16 


17 


13 


1 


12 


8 


14 


14.5 


3 


9 


12 


13 


14 


23 


8.5 


17.5 


17 


15 


15 


19.5 


13 


11 


13 


14 


14 


14 


2 


21.5 


17.5 


8.5 


11 


13 


18 


21 


13 


10 


13 


15 


22 


24 


17 


13 


14 


14 


19.5 


9.5 


17 


20 


18.5 


19 


16 


23 


14 


10.5 


22.5 


16 


17 


16.5 


17 


9.5 


15 


16.5 


18 


17 


24 


15 


23 


17 


18 


13 


23 


21 


19.5 


24 


16.5 


23 


18 


14 


21 


13.5 


6.5 


21 


18 


24 


" 


9.5 


17 


22 


17 


19 


18 


12 


21.5 


19 


14 


19 


6.5 


19.5 


11 


22.5 


13 


16 


20 


3 


17 


17 


22.5 


19.5 


22 


22 


22 


12 


21 


5 


15 


21 


20.5 


19 


10.5 


24 


19.5 


24 


16.5 


8 


17 


22.5 


23 


22 


22 


18 


18 


20 


20 


23 


23 


13 


17 


22.5 


12 


13 


20 


23 


18 


13 


19 


11 


22 


20.5 


21 


24 


19.5 


17 


18.5 


21 


24 


20.5 


22 


24 


21 


24 


20.5 


13 


23 


24 


17 


20 


24 



30 Variation Within the Grades 

TABLE XVIb 
Fifth Grade (V) 

Rank of Pupils in the Different Tests 









U 


o 


TS 


CO 




bt 








c 
ft 


s 

1^ 


o 


s 


s 


2 




M 


-o 


CQ 


13 


>> 






CQ 


CO 


c 
o 


CO 

S-i 


'5 


O 

£ 


O 


u 

s 


o 


a 


c4 


^ 


>. 


O 


0) 


01 


9} 


W 


W 


EH 


<: 


J 


s 


s 


O 



O 0} C 

fc^ ^ t/j ^ — • #** S_i !■ 1_J h^ ^ '^ OS 



1 


2 


2 


7 


2 


9 


4 


1 


1 


6 


4 


9 


2 


11.5 


2 


2 


3.5 


1 


2 


3 


3 


10.5 


4 


2.5 


20 


8.5 


4 


1 


1 


4 


3 


1 


3 


2 


7.5 


3 


5.5 


10 


4 


1 


1 


1 


7.5 


9.5 


1 


4 


8 


4 


7 


16 


17.5 


13.5 


3 


6.5 


4 


14 


7 


5 


2 


8 


5 


3.5 


8 


2 


1 


4.5 


7 


2 


2.5 


10 


5 


6 


3 


1 


3 


6 


6 


5 


16 


5.5 


3 


1 


12 


6.5 


12 


12 


2.5 


10 


11.5 


5 


7 


5 


11.5 


7 


7.5 


14 


2.5 


5 


10 


2.5 


8.5 


5 


5 


7.5 


6 


8 


11 


6 


16 


5.5 


4.5 


5.5 


6.5 


8.5 


20 


6 


2.5 


7.5 


7.5 


7 


9 


12 


15 


23 


13 


14 


18 


20 


11 


2.5 


3 


19.5 


5 


3 


13 


10 


7 


18 


16 


22.5 


19.5 


16 


11 


15.5 


8.5 


10 


8 


13 


6 


10 


11 


9 


9.5 


7 


11.5 


9 


25 


8 


5 


17 


2 


10 


13 


5 


9 


12 


10 


14 


16 


11.5 


14 


22 


14 


8.5 


11 


16 


14.5 


19 


16.5 


15 


13 


20 


16 


16 


4 


9 


10.5 


17.5 


22 


15 


19 


19.5 


18 


9.5 


16 


14 


15 


11.5 


16 


10 


11.5 


10.5 


9 


15.5 


8.5 


7 


21 


10 


22 


12 


15 


21 


17 


16 


20 


6.5 


10.5 


6.5 


14 


22.5 


13 


11 


10 


15 


14 


16 


14 


9.5 


16 


21 


16 


8 


15 


18 


12 


15 


23 


21.5 


19 


17 


17 


13 


7 


7 


19 


6.5 


18 


21 


13 


10 


11 


13 


16 


19 


11 


18 


16 


13 


23 


22.5 


21 


18 


22.5 


17 


17 


20 


16.5 


13 


16.5 


19 


19 


19 


22 


16 


14 


24 


23.5 


19 


19.5 


6 


21 


12 


15 


24 


20 


20 


18 


19 


16 


9 


23 


23.5 


22.5 


23 


17 


22 


18 


17 


21 


22 


21 


17 


21 


16 


15 


11.5 


15 


13 


12 


14 


17 


16.5 


21.5 


13.5 


18 


22 


22 


23 


23 


17.5 


19.5 


20 


16 


24 


24 


18 


22 


23 


13.5 


21 


23 


24 


20 


7 


24 


22 


13.5 


17.5 


21 


22.5 


23 


24 


20 


23 


24 


24 


23 


24 


7 


17.5 


17.5 


21 


24 


19.5 


20 


24 


14.5 


24 


19 


23 






Variation Within the Grades 31 

TABLE XVIc 
Sixth Grade (VI) 

Rank of Pupils in the Different Tests 



u 



o 



I 5 ^ «• K I S 

< < '% oi § t ^ 

•■^ -r I ^ g S " 

3 2 c c o 2 'S 

O ^ ffi W e < h:! 





bo 










c 








c 










o 


73 


c 




X 




7^ 


o 


'jj 


c 


_e8 

"a; 




"ft 


O 




C 


i. 


s 


a 


c 


cS 


^ 


o 






O 


O 


O 


[X. 



1 


2 


10 


8 


2.5 


10 


3 


2.5 


1 


1 


13 


2.5 


1.5 


3 


2 


2 


1 


1 


3.5 


7.5 


1 


3 


5.5 


1 


8 


4 


4 


1.5 


15 


1 


3 


3 


2 


8 


7.5 


14.5 


21.5 


7 


3.5 


11 


8 


18 


8.5 


11.5 


6 


4 


4 


3 


8 


2.5 


14.5 


1 


9 


5 


13.5 


2 


6 


5.5 


6 


3 


5 


5 


7 


14.5 


20 


14.5 


25.5 


12.5 


18.5 


22 


5 


1 


26.5 


18 


10 


6 


6.5 


6 


3.5 


10.5 


4 


25.5 


2.5 


10.5 


17 


6 


15 


8.5 


6 


5 


7 


8 


4 


3.5 


21 


14.5 


15 


8 


23 


5 


3 


7 


3.5 


6 


4 


8 


27 


16 


23 


22 


8 


11.5 


24 


10.5 


29.5 


20 


5 


8.5 


25 


20 


9 


14 


9 


8 


2.5 


25.5 


9 


12.5 


2 


5 


7 


15 


12 


23 


7 


10 


9 


5 


14.5 


25 


2 


21.5 


4 


6 


2 


14 


10 


20 


26.5 


8 


11 


30 


29 


14.5 


9 


24 


11.5 


1 


8.5 


13.5 


9 


25 


3.5 


1 


12 


12 


21 


20 


23 


16 


14.5 


11.5 


12.5 


16.5 


15 


19 


2.5 


5.5 


28 


14 


13 


13 


18 


14.5 


2.5 


19 


25.5 


12.5 


8.5 


5 


1 


8 


16 


26.5 


11 


14 


11 


14 


14.5 


29.5 


19 


3 


15 


21 


25 


18 


19.5 


12 


23 


16 


15 


16 


13 


23 


6 


10 


14 


26 


28 


5 


26.5 


19.5 


26.5 


11.5 


18 


16 


23 


11 


14.5 


12 


22 


21.5 


19.5 


27 


22 


24 


26 


23 


3 


23 


17 


6.5 


30 


28.5 


14 


4 


5 


22 


3.5 


8 


17 


12.5 


20 


11.5 


9 


18 


.18 


25 


14.5 


27 


14.5 


7 


29 


15 


8 


15 


30 


12 


18 


21 


19 


10 


15 


3.5 


25 


22 


18.5 


5.5 


20 


22 


10 


11 


14.5 


18 


15 


20 


29 


23 


14.5 


17 


6.5 


25.5 


19.5 


14 


19 


25 


12.5 


24 


18 


25 


21 


24 


27 


23 


18.5 


19 


7 


22 


8.5 


11 


28 


22 


17.5 


18 


24 


22 


18 


7 


8 


2.5 


25.5 


7 


25 


12 


29.5 


12 


29 


22 


21 


22 


23 


20 


8 


23 


18.5 


29 


18.5 


17.5 


26 


27.5 


11 


27 


26.5 


23 


27 


24 


22 


28 


23 


10.5 


10 


28 


10 


13 


26 


21.5 


11 


17.5 


11.5 


19 


25 


18 


12 


30 


14 


27 


29 


30 


29 


27.5 


30 


15 


29.5 


8 


29 


26 


15 


19 


1 


23 


4 


11.5 


22 


24 


22 


16 


23.5 


8.5 


11.5 


13 


27 


25 


24 


23 


28 


30 


30 


16 


25 


22 


23 


17 


20 


29 


28 


28 


26 


21 


23 


5 


6.5 


17 


17.5 


16.5 


13.5 


26.5 


28 


14.5 


3 


17 


29 


12 


22 


23 


14 


28 


21.5 


27 


22 


17 


21.5 


23.5 


26.5 


11.5 


26 


30 


28 


26 


28.5 


29.5 


22 


16 


28 


30 


17 


29 


21 


29.5 


30 


30 



32 



Variation Within the Grades 



TABLE XVId 
Seventh Grade (VII) 

Rank of Pupils in the Different Tests 



a 
o 


i 

< 

u 


< 

O 






c 

O 


to 

•sx 

Sm 


u 
o 

'So 


-o 
u 
o 

o 


'Si 

5 

>. 

u 
o 

£ 


c 
w 


c 

'5 
n 

u 


o 

% 

"a 

s 


1 

a 


j3 




o 


O 








>> 


o 


a; 


v 
S 




o 


o 

o 


a 
O 


£ 


1 


2 


1 


4 


1 


1.5 


5.5 


6 


5.5 


1 


17 


1 


1 


11 


2 


2 


9.5 


4 


4 


13 


11 


1 


7 


7 


5 


6 


16.5 


2.5 


2 


4 


3 


16 


3 


11.5 


23 


5 


12 


8.5 


2 


9 


22 


13 


4 


24.5 


10 


4 


1 


2 


4 


5 


5 


3.5 


2.5 


3.5 


9 


5 


4.5 


6 


1 


1 


5 


6 


6 


20.5 


4 


2.5 


9.5 


2.5 


3.5 


9 


4 


18.5 


11.5 


13 


7 


6 


12.5 


12 


11.5 


2 


1 


9.5 


1 


1 


9 


7 


2 


2.5 


6 


3 


7 


5 


5 


11.5 


6 


2.5 


13.5 


4.5 


16 


23.5 


17 


3 


5 


4 


5 


8 


3 


8 


20.5 


14.5 


20 


15.5 


2.5 


8 


3.5 


15 


8 


16 


7 


9 


9 


12.5 


17 


20.5 


28 


22.5 


24 


21.5 


5.5 


9 


15 


14.5 


16 


3 


17 


10 


16 


24 


30 


12 


7.5 


21 


10 


17.5 


3.5 


20 


10.5 


7 


26.5 


12 


11 


16 


20 


27 


10 


14 


18 


15.5 


13 


12.5 


18 


23.5 


10 


16 


14 


12 


4 


9 


11.5 


3 


16 


9.5 


4.5 


9 


6 


13 


6 


8.5 


5 


6 


13 


18.5 


14 


27 


25 


5 


26 


8.5 


17.5 


16.5 


25 


16.5 


16 


17 


18 


14 


9.5 


7 


11.5 


14.5 


20 


7 


12 


4 


2 


8 


8 


8.5 


15 


8 


15 


24 


18 


20.5 


24 


11 


9.5 


26 


20 


20.5 


24 


12 


16 


28 


24 


16 


8 


11 


20.5 


11 


22.5 


18 


24 


27 


23.5 


15 


20 


23 


8.5 


16 


17 


30 


30 


1 


16.5 


9 


18 


23 


22 


23.5 


27.5 


21.5 


21.5 


11 


20 


18 


22 


25 


27 


7 


29 


23 


19 


12 


16.5 


26 


30 


24 


14 


26 


19 


21 


11 


27 


29 


17.5 


22 


14 


19 


16.5 


16 


23.5 


19.5 


26.5 


23 


20 


26 


17 


4 


30 


30 


29 


30 


21 


30 


29 


26 


25 


30 


30 


21 


24 


29 


11.5 


21.5 


14 


15.5 


11 


24 


20.5 


3 


18.5 


19.5 


18.5 


15 


22 


18.5 


13 


11.5 


20 


11 


5 


18 


15 


23.5 


19 


8 


11.5 


22.5 


13 


23 


24 


21 


11.5 


21.5 


27 


13.5 


27 


10 


16.5 


9 


4.5 


28 


20.5 


19 


24 


27 


19 


11.5 


9 


20 


2 


13 


11 


16.5 


12 


14.5 


16 


11 


11 


25 


11 


16 


4 


18 


27 


27 


15.5 


28 


26 


11 


26 


26.5 


18.5 


25 


26 


7 


15 


20.5 


27 


24.5 


28 


28.5 


25.5 


27 


27.5 


26 


30 


29 


29 


27 


29 


28 


11.5 


26 


17.5 


6 


17 


25.5 


28.5 


30 


10.5 


13 


8.5 


21 


28 


14 


23 


27 


8 


14 


30 


20 


23 


12.5 


14 


29 


21.5 


22.5 


22 


29 


20 


26 


20.5 


19 


27 


20 


21.5 


29 


16.5 


21 


28 


26.5 


20.5 


27 


30 


28 


22 


20.5 


16.5 


24.5 


25 


28.5 


30 


28.5 


23 


21.5 


29 • 


24.5 


28 



Tables XVIa to XVId, inclusive, give the position each 
pupil holds in his grade in the tests. In addition, the tables 
give a final rating based upon those of the individual tests. 
This final rating gives the position each pupil holds with re- 
spect to the tests as a v^hole. This rating was secured by 
adding the numbers representing the position each child 
held in each of the tests. The sums thus secured were ar- 
ranged from smallest to largest and the final rank of each 
pupil determined. It should be noticed that 43 individual 
measures contribute in the determination of the final rank 
of each pupil in the fourth grade and 48 in the case of the 
pupils in the other grades. 

Table XVIa summarizes for the fourth grade the relation 
between achievement and teachers' judgment. An exami- 
nation of the table shows that one pupil of G. 1 made a rank 
which would place him in G. 2, while one member of G. 2 



Variation Within the Grades 33 

holds second place for the whole grade and should be placed 
in G. 1. Three pupils in G. 3 are inferior in position to 
three others in G. 4. Pupil number 1, who was rated as 
best by the teachers, stands fifth in achievement as meas- 
ured by the tests. 

Table XVIb gives the position each pupil of the fifth 
grade secured in the tests. It is seen that there is consider- 
able variation from the rank given by the teacher. One pu- 
pil of G. 1 makes scores such as to place him in G. 2, while 
two pupils of G. 2 fall in G. 3 and one of G. 3 in G. 4. Pupil 
7 of G. 2 makes scores which would place him in G. 1. 
Likewise pupils 14 and 17 of G. 3 and pupil 21 of G. 4 make 
scores which would place them in higher groups. 

The relative positions held in the tests by the members 
of the sixth grade are shown in Table XVIc. Pupils num- 
ber 5, 8, and 16 are given a much lower position when meas- 
ured by the tests, while pupils number 17, 26, and 28 secure 
much higher ranks. It is seen that pupil number 26 be- 
longs in G. 2, while several others of G. 4 should be placed 
in G. 3. On the whole, it appears that the teachers were 
able to rate with more accuracy the better pupils of the 
grade. 

Table XVId presents the rank each pupil of the seventh 
grade achieved. Pupils number 12, 14, 21, 24, and 27 
achieve much higher ranks than those given by the teach- 
ers. Likewise pupils number 3, 8, 9, 15, 18, and 20 are 
given much lower ratings when measured by the tests. On 
the whole, there is a fairly close relationship between teach- 
ers' judgment and achievement in the tests. A correlation 
between the two, in case of this grade, gives a positive cor- 
relation of 74. 

TABLE XVII 

Coefficients of Correlation — Educational Tests 

C C 

•-i ^ bo 1-1 :s bo bs 

•B ■ >■• "c^ S« ^^ 'c^ .«« 

^■S S5 Si S'-S "2^ £"-5 S2 

3.ti §.ti oC Ccs gaj oce t-13 

ot- >i^ X™ !6w ™a J3a> >>ft 

0< ^< HS ^P3 Km HPh <m 

Courtis Arithmetic 74 36 53 21 46 39 

Woody Arithmetic 74 37 47 23 43 43 

Thorndike Handwriting __ 36 37 23 12 29 42 

Kansas Silent Reading 53 47 23 07 44 52 

Thorndike H. Speed 21 23 12 07 27 20 

Thorndike Reading 46 43 29 44 27 47 

Ayres Spelling 39 43 42 52 20 47 

The relation between the results of the several educa- 
tional tests are summarized in Table XVII. It should be 



34 Variation Within the Gi^ades 

noticed that these are the average coefficients secured from 
the four grades. Owing to the fact that the fourth grade 
did not take all the test, only three coefficients were used 
in a few cases in determining averages. In order to deter- 
mine which of the tests holds the closest relationship to the 
other tests, we have added each of the columns given in the 
tables. The average correlation of each test with the other 
six tests is : 

Courtis Arithmetic with the other tests 45 

Woody Arithmetic with the other tests 44 

Thorndike Handwriting (Legibility) with the other tests 30 

Thorndike Handwriting (Speed) with the other tests 18 

Kansas Silent Reading with the other tests 38 

Thorndike Reading with the other tests 39 

Ayres Spelling with the other tests 40 

It is seen that the arithmetic tests correlate highest with 
the other tests. The reading and spelling tests come next, 
with practically equal averages. The handwriting test cor- 
relates lowest. 

TABLE XVIII 

Coefficients of Correlation — Raw — The Mental Tests 

; « — ■ 

o c 



o 






"g cl c-^ S -His a S 

^1 II 1-^ s 1^ i S 



Logical Memory 66 54 54 46 75 48 

Memory Words 66 54 66 61 63 46 

Memory Digits 54 54 38 38 52 37 

Cancellation 54 66 38 42 47 40 

Word Building 46 61 38 42 53 40 

Completion 75 63 52 47 53 51 

Opposites 48 46 37 40 40 51 

Table XVIII summarizes the relation between the results 
of the various mental tests. The coefficients given are the 
average coefficients secured from the results of the .four 
grades. By adding each of the columns of the table and 
securing an average, we are able to determine the degree of 
relationship each of the tests bears to the other tests. The 
average coefficients of correlation of each of the mental tests 
with the other six is : 

Logical Memory with the other tests 57 

Rote Memory for Words with the other tests 59 

Rote Memory for Digits with the other tests 42 

Cancellation with the other tests 48 

Word Building with the other tests 47 

Completion with the other tests 60 

Opposites with the other tests 44 



Variation Within the Grades 35 

From the several tables it is seen that here is a fairly 
high correlation between ability in one test and ability in 
the other tests — that is, the pupils who make high scores in 
one test tend to do well in the other tests. The same fact is 
true with reference to the educational tests. Pupils who 
excel in one subject tend to lead in the others also. If we 
compare ability in the mental tests with achievement in the 
educational tests, we find that the pupils making the best 
scores in the mental tend to lead in point of achievement in 
the educational tests. 

TABLE XIX 

Correlation Between Final Rank in the Educational Tests and 
Final Rank in the Mental Tests 

Fourth Grade 69 

Fifth Grade 74 

Sixth Grade 68 

Seventh Grade 76 

Average 72 

The relation between achievement in the educational tests 
and ability as measured by the mental tests is presented by 
the coefficients above. The final rank of each pupil in the 
educational and mental tests was used in securing these co- 
efficients. It should be noticed that the coefficients repre- 
sent the relation between 14 individual educational meas- 
urements on one hand and 34 on the other. It is seen that 
there is a very decided correlation between achievement and 
ability as thus measured. 



PART IV 

Comparison of Results With Those Obtained by Others 

One of the earliest attempts to study the relation between 
ability and school progress was that of Binet ('99). He 
made a rather intensive study of the relation of voluntary 
attention to class standing. Eleven pupils were used in 
the study. Five of these were classed as bright and six as 
dull. Rather simple tests were used. 

Binet concludes that the difference between bright and 
dull pupils lies in the fact that bright pupils are able to 
adjust themselves to a situation more quickly than dull. 
He believes that this difference is greater at first than at 
the end — that is, the bright children respond more quickly 
at first, but that the dull children adapt themselves to the 
situation in time, only more slowly. This would imply that 
bright and dull pupils are farther apart at the beginning of 
a task than at the end. 

Carmen ('99) measured 576 pupils in the public schools 
of Saginaw, Mich., with reference to strength of grip and 
least sensibility to pain. These pupils ranged from 10 to 
14 years of age. First, the names of the bright and the dull 
pupils were secured from the teachers. These were placed 
into two groups — one good and one poor. The bright pu- 
pils had a greater strength of grip except in the case of the 
left hand for the boys. Here the dull group seemed to be 
superior. Since the bright and dull pupils were not sep- 
arated according to age, too much weight cannot be at- 
tached to the results; for Carmen found that sensibility to 
pain decreased with age, and, of course, strength increases 
with age. 

Smedley ('00) compared the standing in school of twelve- 
year-old pupils scattered through the grades of the Chicago 
public schools with respect to motor performance. He 
found that the twelve-year-old pupils of the higher grades 
were decidedly superior in stature, weight, strength of 
grip, endurance, and vital capacity to those found in the 
lower grades. His results show that on the average the 
bright pupils are superior physically to the dull ones. 

Gesell ('05) studied handwriting as related to school in- 
telligence. He secured a large number of handwriting 
specimens. These specimens were divided into four groups, 
as follows : 

Gfoup I. Specimens from the three best writers in the 
grade. 



Variation Within the Grades 37 

Group II. Specimens from the three poorest writers in 
the grade. 

Group III. Specimens from the three pupils of the highest 
mental ability in each grade as represented by school stand- 
ing. 

Group IV. Specimens from the three pupils of the lowest 
mentality in each grade as represented by the class standing. 

The pupils in these groups were rated as to school intel- 
ligence, general intelligence, motor ability, and facility in 
writing. Gesell concludes that for a large number of chil- 
dren handwriting varies directly with school ability. 

Bolton ('03) studied the relation of motor power to in- 
telhgence. He used as his subjects 120 children in the pub- 
He schools of Lincoln, Neb. Sixty of these children came 
from the best homes of the city and sixty came from the 
poorer districts. He characterized these two groups as his 
good and poor groups. Notwithstanding the fact that he 
selected the children so as to have equal age groups, the 
good group averaged two grades higher than the poor. 
Tests of voluntary control (the tapping test), steadiness 
in standing, and steadiness and precision in moving either 
hand were used. 

The good children surpassed the poor in every trial. Not 
only were the good children superior, but this superiority 
seems to increase with age. The gap between the good and 
poor nine-year-old children was much wider than that be- 
tween the good and poor eight-year-old ones. Bolton con- 
cludes that, with bright children, motor power increases 
with age. He says: 'There is greater rapidity of motion, 
increased steadiness, and nicer precision the older the chil- 
dren grow. Backwardness, slowness of growth, and arrest 
of development are indicated by pupils through their infe- 
riority to their fellows of the same age." While all these 
tendencies are noticeable, probably the most striking fact 
is the amount of fluctuation shown by the poor children. 

Terman ('06) has attempted to differentiate bright pu- 
pils from dull by studying the ability of fourteen boys at 
"eight more or less different points" — namely, (1) their 
powers of creative imagination or invention, as tested by 
the ability to solve puzzles; (2) their logical processes; 

(3) their mathematical ability, as tested by the ability to 
solve arithmetical problems requiring original thinking; 

(4) language ability, as tested by spelling, word building, 
reading, completion tests, and ease in interpreting oral 
commands; (5) their insight as revealed in the interpre- 
tation of fables; (6) rapidity in learning, as revealed in 
learning the game of chess; (7) memory abilities, as shown 



38 Variation Within the Grades 

by memory for geometrical forms, moves in chess, steps in 
the solution of puzzles, and for connected ideas; and (8) 
their motor ability, both general and in the acquisition of 
new forms of behavior. He used a great many and varied 
tests, but in the main they formed a connected group. 

The subjects selected were considered by their teachers 
as among the brightest or dullest boys that could be found 
in the city of Worcester. Seven bright and seven dull boys 
were used in all the tests. 

It is very hard to evaluate with any degree of accuracy 
the records made by the subjects. Specific compai-isons 
cannot be made, owing to the fact that the number of sub- 
jects was very small, that the tests used were new, and that 
few of the tests used have since been standardized. Again, 
"bright" and ''dull" are only relative terms and give us no 
notion as to the comparative standing of the two groups 
with reference to school intelligence. Subject to these lim- 
itations, however, Terman found that most of his tests did 
clearly differentiate between the bright and dull boys. 

Terman concludes that the bright group of boys is supe- 
rior to the poor group in all tlie mental tests, but inferior 
in the motor tests. This superiority of the good group 
seems to be about the same in all the mental tests except 
those falling under the head of invention, where there seems 
to be only slight, differences. The superiority of the dull 
group of boys over the bright group in the motor tests 
seems to be hardly characteristic of people in general. If 
so, it means that there is a negative correlation between in- 
tellectual and motor ability. This seems to be in conflict 
with the results secured by other investigators. Smedley 
COO), Bolton ('03), and others have found that "good" 
children were superior to "poor" children in motor ability. 

Bonser ('10) made a very extensive study of the capacity 
of grammar-school children for those forms of thinking 
which are commonly called "reasoning." His subjects were 
757 children of the fourth, fifth, and sixth grades of the 
public schools of Passaic, N. J. He used a series of tests 
which he thought would exercise four of the most 
fundamental phases of purposive thinking — namely, the 
mathematical judgment, controlled association, selective 
judgment, and that complex process used in the interpre- 
tation of literature. Bonser felt that the tests really sub- 
jected the pupils to nearly all forms of purposive thinking. 
He says: "These pupils have been subjected to various 
forms of each of the four types of reaction which furnish 
a measure for four somewhat overlapping and related, 
though quite complex, forms of purposive thinking. It is 



Variation Within the Grades 39 

believed that measures of these qualities, properly related, 
will provide fairly reliable measures of what we usually 
mean by reasoning ability." 

Bonser wishes to show that within the grades the younger 
pupils were equal to or exceeded older ones in median abil- 
ity, and his results seem to bear him out in this conclusion. 
In 24 cases out of 36 the youngest 25 per cent of the pupils 
in the grade equaled or surpassed the median ability of the 
oldest 25 per cent. In 27 cases out of 36 the median ability 
of the youngest 25 per cent of the pupils equaled or sur- 
passed the median ability of the whole grade. Bonser's 
results show clearly that there are two well-defined groups 
in every large grade — first, those who for various reasons 
are retarded, and, second, those who are accelerated or 
more advanced in mental ability. Furthermore, this ac- 
celerated younger group seems to surpass the retarded older 
group in ability and to equal at least the median ability of 
the whole grade. 

A further interesting fact is shown by Bonser's results. 
In studying the youngest and oldest groups, comparison is 
made between groups of unequal ages. When groups hav- 
ing the same median age, but of different grades, are com- 
pared, the same results are found as when the youngest and 
oldest groups within the same grade are compared — that is, 
the youngest group in each grade surpasses in median abil- 
ity the whole group immediately lower, but having approx- 
imately the same age. 

Lapie ('12) studied several groups of children. He 
found in every class a small number of children who were 
advanced for their age and also a small number w^ho were 
retarded. From these two groups he selected 24 pupils — 
23 boys and 1 girl — for his study. The advanced ones 
ranged from 8 years and 6 months of age to 11 years ; the 
retarded, from 12 to 14. These two groups were further 
divided into subgroups — A2, Al, Rl, and R2. The A2 
group contained all the pupils accelerated by more than two 
years, the Al group contained all those accelerated a year 
or less, the Rl group contained all those retarded a year or 
less, and the R2 group contained all those retarded more 
than one year. Six pupils were placed in the A2 group, 
7 in the Al group, 5 in the Rl group, and 6 in the R2 group. 

The most unfavorable element connected with the experi- 
ment was the age difference. It is practically certain that 
the results are not what they would have been had equal 
age groups have selected. The results secured from most, 
if not all, mental and physical tests are affected by the 
age factor. It should be noted, however, that the age differ- 



40 Variation Within the Grades 

ences were so distributed as to give the advantage to the 
duller group. The differences brought out by the mental 
tests have more significance because of this age difference. 

Lapie says that the advanced groups not only respond 
more rapidly, but that their ideas have more logical con- 
nections than do those of the retarded group. "The re- 
tarded seemed to digress from the train of thought more 
than the accelerated. Their attention could not be kept on 
a single line of thought, but was constantly shifting from 
one external perception to another." The accelerated pu- 
pils not only had a greater number of associations, but the 
most marked difference between the groups was in respect 
to the types of associations. Associations due to the simi- 
larity in appearance or sound of two words were more fre- 
quent with the retarded groups, while associations due to 
logical connections were more frequent with the accelerated 
groups. The retarded groups frequently responded to a 
stimulus word by naming some object present to the senses. 
The accelerated groups seemed to be more able to hold their 
attention on the problem in hand and to respond with ideas 
having some logical connection with the stimulus word. 

As a further study, Lapie examined the physical condi- 
tions of the children and the economic and social conditions 
of their homes. Taking into account all the differences in 
development due to differences in age, he believes that the 
advanced pupils are developed better for their ages than the 
retarded for theirs. This difference, he explains, may be 
due to the fact that the advanced pupils were well nourished, 
while the retarded pupils came from homes not in good 
economic circumstances. In his study of the home condi- 
tions, he found that one pupil from group A2 came from 
a home of just moderate economic circumstances. The 
other members of the group were the children of teachers 
or merchants. Here he found small families, no family 
having more than two children. The parents of the Al 
group were of slightly less economic independence. The 
majority were small merchants or employees of the rail- 
road. The number of children in these homes ranged from 
two to five. In the homes of the Rl group the economic 
conditions were worse and the families larger, the number 
of children ranging from five to nine. Although the par- 
ents of this group had larger families, their revenues were 
smaller. Poverty was found to rule in the families of the 
R2 group. Here alcoholism had consumed a good part of 
the total family revenue. Large families with a high death 
rato and poor economic and social conditions characterized 
the homes from which the retarded groups came. Small 



Variation Within the Grades 41 

families, a low death rate, and good economic and social 
conditions were characteristic of the homes from which the 
accelerated pupils came. 

By way of summary, Lapie says that the study seems to 
point out the fact that accelerated pupils are of superior 
ability at every point. Moreover, he believes that this su- 
perior mental ability is accompanied by or has its founda- 
tions in a vigorous physical condition. Furthermore, he 
found that mental and physical superiority usually went 
along with good economic, social, and moral conditions. 

Lapie is correct in that inferior physical and mental 
abilities are generally found where poor economic, social, 
and moral conditions prevail. But the inference that these 
inferior abilities are the result of poor economic, social, and 
moral conditions is hardly justifiable, to say the least. In- 
ferior mental and physical abilities, poor economic, social, 
and moral conditions, are more likely the result of poor 
hereditary equipment. 

Keys ('11) made a rather extensive survey in his attempt 
to locate accelerates and arrests in the grades. He esti- 
mated that one-fourth of all the pupils in our grades were 
potential accelerates. He believes that deportment, the ab- 
sence of physical defects or superior physical ability, and 
regular attendance, all play an important role in success in 
school work. Keys was unable to determine how far con- 
duct influenced the teacher in grading on school subjects 
and how far good school work influenced the teacher in 
rating the pupils in conduct. He believes that they mutu- 
ally influence each other. The conduct rankings would seem 
to be a fairly good index as to how far the pupils fit into the 
spirit of the work. It is very likely true that children 
whose conduct is good are freed from many irrelevant 
things that hinder progress in the grades. Keys found that 
the accelerated pupils received higher conduct grades .than 
any other class except the honor class. 

Winch ('06) studied the relations existing between ''rote" 
memory and proficiency in school subjects. He selected 6 
girls from the upper half and 6 from the lower half of the 
same grade. There were 65 girls in the grade. He used 
ten sets of consonants as the memory material. He lays 
stress on the suggestion that general intellectual proficiency 
is usually accompanied by good memory. It appears that 
the only girl among his subjects in the upper section with a 
low memory score is much older than the other girls in that 
section. In the lower section there is, however, one sub- 
ject (D. R.) whose good memory score is not accompanied 
by high position in class. Winch concludes as follows: 



42 Variation Within the Grades 

(1) That pure memory improves with age within the limits 
chosen, but principally in so far as increased age itself im- 
plies increase of general intellectual proficiency; and (2) 
that there is generally a direct relation between **good 
memory" of this kind and intellectual proficiency, so far as 
this can be measured by success in school subjects. 

Kelley ('14) investigated the records of 59 grammar- 
school students who had passed on to the high school. He 
found the coefficient of correlation between the first-year 
standing in high school and the average grades received in 
the fourth grade to be 62. This, together with the fact that 
some of the pupils had skipped grades, led him to say that 
there is strong evidence that natural capacity is a very 
much more important factor than training in determining 
relative scholastic standing. In fact, he found the correla- 
tion between an estimate of the pupil's ability to do high- 
school work made when the pupil is in the fourth grade to 
be nearly as accurate as one made when the pupil is in the 
seventh grade. This leads one to feel that it is very impor- 
tant that an adequate record of each grammar-school pupil's 
ability and attainment be kept. 

Terman ('15) studied the relation of school success to 
intelligence. His data were by-products of the study of 
the school success of 1,000 nonselected school children who 
were tested in 1914-1915 by the Stanford Revision of the 
Binet-Simon measuring scale of intelligence. The study 
deals principally with the correlation between the intelli- 
gence quotient and grade progress. No child with a men- 
tal age below 8 was included in the study. 

Terman found a rather surprising disagreement between 
grade progress and mental age. Of the 1,000 children, 85 
were retarded two or more grades below the norm for 
their mental age. Of the 85, 23 per cent were actually ac- 
celerated by chronological age. Only 8 per cent of those 
who were retarded two years or more according to mental 
age were retarded as much as two years by chronological 
age. Comparison of grade status with mental age and 
chronological age revealed the fact that the grade location 
of children does not fit their mental age much better than 
their chronological age. 

To summarize, Terman found : 

1. That the range of distribution over the grades by men- 
tal age, although less than by chronological age, was very 
great. 

2. That, compared to his possibilities, the child of excep- 
tionally superior intelligence is almost always retarded, be- 
cause teachers are prone to promote by chronological age 



Variation Within the Grades 43 

rather than mental. His work is nearly always superior, 
and the evidence suggests strongly that this superiority of 
school work would continue even if extra promotions were 
granted. 

Wallin ('11) studied the relation of spelling efficiency to 
sex and age. In the Cleveland schools he found the girls 
to be more proficient than the boys. The difference be- 
tween the gross averages for all the schools amounted to 
2.1 per cent. He concludes that the girls' superiority is 
mostly on the side of verbal memory. 

He compared the normal pupils with the accelerated and 
retarded with respect to proficiency in spelling. The ac- 
celerated pupils, although younger than the normal, sur- 
passed them in spelling ability. Likewise the retarded pu- 
pils, although older than the other members of the grade, 
were the least efficient. 

Mead ('16) studied the relation of intelligence to certain 
mental and physical traits. His data were secured from 
measurements taken of 430 feeble-minded children and 480 
normal children. The following relations were studied: 
(1) Age of walking and talking in relation to general intel- 
ligence, (2) the height and weight of the children in relation 
to general intelligence, (3) strength of grip and dexterity 
in relation to general intelligence, (4) perception and mem- 
ory in relation to general intelligence. 

He summarizes his study by saying that normal children 
are better at each age studied than mentally defective chil- 
dren. Sexes differ less with the feeble-minded. ''Defec- 
tive children occupy the lower end of a large distribution 
curve for children in general." The best mental powers 
which defective children are likely to bring to school are 
those of perception and memory. 

Pintner ('18) has done an exceedingly valuable piece of 
work in devising norms by which a mental survey may be 
made. During his preliminary work in establishing norms, 
the children in a number of schools were tested. Great 
variability of the mental index in the different grades of 
the same school was found. A mental index of 58.5 was 
found for one school, while an index of only 17 was found 
for another. 



PART V 

Summary and Conclusions 

A. As to Procedure. — In this study, four grades, com- 
posed of 108 pupils, have been studied rather intensively. 
The grades selected for the study are. undoubtedly much 
above the average both in point of organization and in- 
struction. Each grade has been arbitrarily divided into 
four groups according to the teachers' estimate of the abil- 
ity of the pupils. The groups of each grade are composed 
of approximately the same number of children, and there 
are but slight age differences between the groups of any 
grade. 

Fourteen educational and thirty-four mental measure- 
ments were taken of the grades. The results have been 
given both in their original and final form. Thus any cal- 
culations may be checked or the data rescored in any man- 
ner desired. 

The following relations and comparisons have been stud- 
ied: 

1. A comparison of the achievement of the brighter or 
duller pupils of the grade with the grade as a whole. 

2. A comparison of the brighter or duller pupils of a 
grade with a similar group in another grade. 

3. A comparison of the achievement of any group within 
a grade with the achievement of the four grades combined. 

4. The relation between accomplishment and accuracy. 

5. The relation between accomplishment in the tests and 
school standing. 

6. The relation between teachers' judgment and accom- 
plishment. 

7. The relation ability in one test bears to ability in the 
other tests. 

B. As to Results. — In general, we have found it highly 
instructive to compare the achievement of the better or 
poorer pupils of a grade with each other or with the grade 
as a whole. The better pupils of a grade frequently, as in 
the arithmetic or logical memory tests, do from 50 to 100 
per cent better than the poorer members of the same grade. 
Frequently the brighter pupils of a grade surpass the aver- 
age attainment of the whole grade by 50 per cent. 

There is considerable overlapping of ability between 
grades. Children with ability equal to the median ability 
of the grade above are found in all our grades. Pupils of 



Variation Within the Grades 45 

exceptional ability in a lower grade often surpass the poor- 
est 25 per cent of the pupils of several grades above. 

A close correlation between accomplishment, as meas- 
ured by the tests, and accuracy, in terms of errors made, 
exists — ^that is, a high degree of attainment has a tendency 
to be accompanied with a like degree of accuracy. The 
better pupils of a grade not only work faster, but also work 
more accurately. In case of a function, as addition, which 
operates in the daily school life of the pupils, it appears that 
the relation between accuracy and attainment is very close. 
This is probably due to the fact that previous practice has 
emphasized accuracy. 

A close relation exists between ability as measured by 
the tests and progress in the grades. A coefficient of 72 
was found between attainment in the educational tests and 
school standing, and one of 68 between ability as meas- 
ured by the mental tests and school standing. 

Pupils who display exceptional ability in one test tend to 
do well in all the tests. A correlation of achievement in 
the educational tests with ability displayed in the mental 
tests, gives a coefficient of 72. In studying the school rec- 
ord of the children, the writer was impressed with the fact 
that a pupil standing near the top in one school subject 
tended to rank high in the other subjects also. 

The data presented suggest that the brighter pupils of a 
grade are able to do much more work than the duller pupils 
of the grade. The fact that the members of a grade differ 
in their hereditary equipment, that some members are able 
to do twice as much work as others, has considerable im- 
portance for the school. It is evident that pupils with dif- 
ferent degrees of ability cannot receive the same instruc- 
tion and yet progress at the same rate. No grade can be 
taught as a whole and its members progress at an even rate. 

If the pace for the grade is determined by the ability of 
the better pupils to progress, the result is that the duller 
pupils are given tasks which they are unable to accomplish. 
They consequently fall farther behind, repeat the grade, or 
drop out of school. If the pace is set by the duller pupils 
of the grade, the better pupils are not compelled to put forth 
their best efforts, and consequently fall into habits of ineffi- 
ciency. 

There is probably little danger of overwork. The poorer 
pupil is in more danger of having the grade progress so 
fast that he is unable to understand and do the tasks set 
for him, while the better pupil is in danger of not having 
enough tasks set for him and consequently of falling into 
apathy and habits of inefficiency. 



46 Variation Within the Grades 

REFERENCES 

Binet ('11) : Nouvelles recherches sur la measure du vivean intellec- 
tual ches les enfants I'ecole — L'Annie. — Psychologique XVII, p. 
169. 

Binet ('99) : Attention et Adaptation — L'Annie. — Psychologique VI, 
p. 248. 

Bolton ('03) : The Relation of Motor Power to Intelligence. — Amer- 
ican Journal of Psychology XIV, p. 351. 

Bonser ('10) : The Reasoning Ability of Children of the Fourth, Fifth, 
and Sixth School Grades. — Columbia University Contributions to 
Education, No. 37. 

Carmen ('99) : Pain and Strength Measurements of School Chil- 
dren. — American Journal of Psychology, October, 1899, p. 392. 

Gesell ('05) : Accuracy in Handwriting as Related to School Intelli- 
gence. — American Journal of Psychology XVII, p. 344. 

Kelley ('14) : Educational Guidance. — Columbia University Contri- 
butions to Education, No. 71. 

Keys ('11) : Progress Through the Grades of the City Schools. — Co- 
lumbia University Contributions to Education, No. 42. 

Lapie ('12) : Advances and Retardes — L'Annie. — Psychologique 
XVIII, p. 232. 

Mead ('16) : Relation of Intelligence to Mental and Physical Traits. — 
Columbia University Contributions to Education, No. 76. 

Pintner ('18) : The Mental Survey. — New York, Appleton. 

Smedley ('00) : Report of Commissioner of Education, p. 1100. 

Terman ('96) : Genius and Stupidity. — Pedagogical Seminary XIII, 
p. 307. 

('15) : The Mental Hygiene of Exceptional Children. — 

Pedagogical Seminary XXII, p. 529. 

('15): The Measurement of Intelligence. — New York, 

Houghton-Mifflin Company. 

Wallin ('11) : An Experimental and Critical Study of the Function 
of Method in the Teaching of Spelling. — Baltimore, Warwick & 
York. 

Winch ('06) : Immediate Memory in School Children. — Br. Journal of 
Psychology, 1906, p. 52. 



Variation Within the Grades 47 

BIBLIOGRAPHY OF TESTS 

Ayres ('15) : A Measuring Scale for Ability in Spelling. — Russell 
Sage Foundation, 

Courtis ('14) : Manual of Instructions for Giving Standard Tests. — 
Department of Cooperative Research, Detroit, Mich. 

Kelley ('15) : Kansas Silent Reading Test. — Kansas State Normal 
Bulletin IV, No. 7. 

Pyle ('13) : The Examination of School Children.— New York, The 
MacMillan Company. 

Strong ('16) : The Effects of Hookworm Disease on the Mental and 
Physical Development of Children, p. 52. — The Rockefeller Foun- 
dation, New York. 

Thorndike ('14) : Teachers' College Record, September, 1914. 

Thorndike ('10) : Teachers' College Record, March, 1910. 

Trabue ('16) : Completion — Test Language Scales. — Columbia Uni- 
versity Contributions to Education, No. 71. 

Whipple ('15) : Manual of Mental and Physical Tests, Complex Proc- 
esses, p. 150, p. 156, p. 207, p. 275. — Baltimore, Warwick & York. 

Woodwarth & Wells ('11) : Association Tests. — Psychol. Rev. Men., 
No. 57. 

Woody ('16) : Measurements of Some Achievements in Arithmetic. — 
Columbia University Contributions to Education, No. 80. 



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